Porosity Classification and Clustering in

Ti-6Al-4V alloy parts fabricated by

Additive Manufacturing

This thesis is submitted to University College Dublin in fulfilment of

the requirements for the degree of Master of Engineering Science

in Mechanical and Materials Engineering.

Conor Sheehan

National University of Ireland

University College Dublin

College of Engineering and Architecture

School of Mechanical and Materials Engineering

Prof. Denis D. Dowling Prof. Kenneth T. Stanton

Principle supervisor Head of school

ABSTRACT

The additive manufacturing of metal alloys by laser powder bed fusion (LPBF),

requires the optimisation of powder melting conditions, in order to achieve the desired

material properties. Reducing the level of porosity incorporated in the alloy is a key

consideration during powder melting. In addition to the overall level of porosity a further

consideration is its type (i.e., Gas, Keyhole and Lack of Fusion), as these in-turn can

also influence the material properties of the printed alloy. This thesis is focused on the

printing of Ti-6Al-4V parts using the Renishaw RenAM 500M, production scale additive

manufacturing system. During part printing argon gas is passed over the print bed in

order to provide a non-oxidising atmosphere, as well as to remove process by-

products. This study includes an evaluation of the effect of varying the argon gas flow

rate on the porosity of the resulting printed alloy. During printing the melting of the alloy

part was monitored using optical emission spectroscopy (InfiniAM system) and a

correlation was obtained between the in-process emission data obtained from the

meltpool and the level of porosity obtained in the printed alloy parts. The latter was

determined using both micro-X-ray-computed tomography (XCT) and optical

microscopy. The latter examination was based on cross sectional studies of the printed

alloy samples. Significantly increased porosity in the alloy was observed when lower

argon gas flow rates were used, during printing.

Unsupervised machine learning algorithms were applied to data obtained from both

the XCT and microscopy examination, to determine if this data could be used to help

determine the effect of gas-flow on the type of porosity generated in the printed alloy

samples. Based on the clustering of XCT data, a high argon gas flow rate exhibited

the largest proportion of pores identified in the build being labelled as ‘gas’ pores, in

comparison with those printed at lower Ar flow rates. The ‘Gaussian Mixture Model’

(GMM), unsupervised machine learning technique was found to be effective in

clustering of porosity data. This machine learning technique facilitated the

quantification of the relative porosity type distribution, within parts printed at the three

argon gas flow levels investigated.

The use of supervised classification ML algorithms were also applied to a set of

manually labelled porosity data obtained using the cross-sectional microscope images

(using ImageJ). The evaluated algorithms include K-Nearest Neighbour, Logistic

Regression, Naïve Bayes, Multi-Layer Perceptron, Decision Tree Classification,

Support Vector Machine, Gradient Boosting, and Extreme Gradient Boosting. This

multiclass classification was implemented in two separate binary classification

problems, firstly as gas / non-gas, and subsequently the non-gas class were classified

as Lack of Fusion / Keyhole. Through comparison of both Gas Flow dataset cross

validation scores, as well as final Test Set Scores, the classification obtained for gas /

non-gas was determined to be the more accurate, compared with that obtained for

Keyhole / Lack of Fusion classification. It was also found that of the eight supervised

ML approaches evaluated, the Extreme Gradient Boosting Model achieved the most

accurate porosity classification.

 
TABLE OF CONTENTS: 
 
CONTENTS 
ABSTRACT ............................................................................................................................. 2 
TABLE OF CONTENTS: ............................................................................................................ 3 
LIST OF FIGURES: ................................................................................................................... 6 
LIST OF TABLES: .................................................................................................................... 9 
ACKNOWLEDGEMENT ............................................................................................................ 11 
CHAPTER 1: GENERAL INTRODUCTION: ................................................................................. 13 
1.1 : INTRODUCTION: .................................................................................................... 13 
1.2 : MOTIVATION:........................................................................................................ 13 
1.3 : PROBLEMS AND OBJECTIVES: ............................................................................... 13 
1.4: THESIS FORMAT:........................................................................................................ 15 
CHAPTER 2: LITERATURE REVIEW: ........................................................................................ 17 
2.1 OVERVIEW .................................................................................................................. 18 
2.2 Additive Manufacturing ........................................................................................... 18 
2.2.2 LPBF PROCESS PARAMETERS .............................................................................. 21 
2.3 DEFECTS AND POROSITY ............................................................................................. 23 
2.3.4 POROSITY IMPACTS ON MECHANICAL PERFORMANCE ............................................. 26 
2.3.5 CHAMBER GAS FLOW IMPACT ON POROSITY ........................................................... 27 
2.4 MACHINE LEARNING IN ADDITIVE MANUFACTURING ....................................................... 28 
2.4.1 ML APPLICATIONS IN AM ...................................................................................... 30 
2.4.2 UNSUPERVISED CLUSTERING................................................................................. 33 
2.4.3 SUPERVISED CLASSIFICATION ............................................................................... 36 
2.5 LITERATURE REVIEW SUMMARY ................................................................................... 41 
CHAPTER 3: EXPERIMENTAL METHODS AND MATERIALS ........................................................ 43 
3.1 INTRODUCTION ............................................................................................................ 43 
3.2 MATERIALS: TI-6AL-4V ............................................................................................... 43 
3.3 RENISHAW RENAM 500M AND INFINIAM IN- PROCESS MONITORING SYSTEM ................ 43 
3.3.1 INFINIAM SPECTRAL ............................................................................................. 45 
3.4 X-RAY COMPUTED TOMOGRAPHY ................................................................................ 45 
3.5 OPTICAL MICROSCOPY EXAMINATION ........................................................................... 46 
CHAPTER 4: POROSITY ANALYSIS RESULTS .......................................................................... 49 
4.1 INTRODUCTION ............................................................................................................ 49 
4.2 COMPARISON OF POROSITY OBTAINED THROUGH XCT AND MICROSCOPY ...................... 49 

3 CONCLUSIONS ............................................................................................................ 52 
CHAPTER 5: UNSUPERVISED CLUSTERING AND CLUSTER NUMBER EVALUATION ..................... 55 
1: INTRODUCTION ........................................................................................................... 55 
2: UNSUPERVISED CLUSTERING ...................................................................................... 55 
3: CLUSTER NUMBER EVALUATION ................................................................................. 57 
3.1: HIERARCHICAL CLUSTERING AND DENDROGRAM APPROACH ................................. 58 
4.2: HIERARCHICAL CLUSTERING RESULTS ................................................................. 58 
3.2: ELBOW PLOT APPROACH ..................................................................................... 60 
4.1: ELBOW PLOT RESULTS ........................................................................................ 62 
3.3: BAYESIAN INFORMATION CRITERION APPROACH ................................................... 63 
4.3: BIC SCORE RESULTS .......................................................................................... 64 
3.4: SILHOUETTE SCORE APPROACH ........................................................................... 65 
4.4: SILHOUETTE SCORE RESULTS .............................................................................. 66 
4: CLUSTER NUMBER RESULTS SUMMARY ...................................................................... 67 
5: UNSUPERVISED CLUSTERING USING GMM RESULTS .................................................... 67 
5.1: GMM PLOT FOR XCT DATA ................................................................................. 68 
5.2: GMM PLOT FOR MICROSCOPY DATA .................................................................... 71 
6: DISCUSSIONS AND CONCLUSIONS ............................................................................... 76 
CHAPTER 6: SUPERVISED CLASSIFICATION AND EVALUATION ................................................. 78 
1: INTRODUCTION ........................................................................................................... 78 
2: SUPERVISED CLASSIFICATION ..................................................................................... 78 
Dataset Description ...................................................................................................... 78 
Classification Implementation....................................................................................... 79 
3: CLASSIFICATION EVALUATION .................................................................................... 80 
3.1: GENERAL ACCURACY .......................................................................................... 81 
3.2: AREA UNDER CURVE (AUC) SCORE AND RECEIVER OPERATOR CHARACTERISTIC 
(ROC) CURVE ............................................................................................................... 81 
3.3: RECALL AND PRECISION SCORES ......................................................................... 83 
3.4: F1 SCORES ......................................................................................................... 83 
4: GAS/NON-GAS 5-FOLD CROSS VALIDATION ................................................................ 84 
5: GAS/NON-GAS TEST SET EVALUATION ....................................................................... 86 
6: KEYHOLE/LACK OF FUSION 5-FOLD CROSS VALIDATION .............................................. 85 
7: KEYHOLE/LACK OF FUSION TEST SET EVALUATION ..................................................... 86 
8: DISCUSSION AND CONCLUSIONS ................................................................................. 89 
CHAPTER 7: CONCLUSIONS................................................................................................... 93 
1 FUTURE WORK ............................................................................................................ 97 
APPENDIX ............................................................................................................................ 78 
BIC SCORES .................................................................................................................... 98 

REFERENCES ..................................................................................................................... 100

LIST OF FIGURES:  
 
Figure 1: GE Aviation fuel injector nozzle for Superalloys. Metal AM facilitates the 
production of more lightweight components in a single print process [10]................ 19 
Figure 2: Cross Section Schematic of a Laser Powder Bed Fusion process at 
machine scale (left) and powder scale (right) [45] .................................................... 20 
Figure 3: Schematic depicting the laser beam and powder bed interaction [53] ...... 21 
Figure 4: Process Parameters in LPBF (also known as SLM) with VED parameters 
highlighted in yellow [63] .......................................................................................... 22 
Figure 5: Differing forms of Porosity formed at the VED values shown in LPBF 
produced components. The insert images help to demonstrate the types of porosity 
generated i.e. LOF (low VED) and KH (high VED). Minimised porosity in the 
highlighted light blue region achieved through minimising both KH pores, and LOF 
pores [63]. ................................................................................................................ 23 
Figure 6: Microstructural pore type morphologies, generated with common (upward) 
build direction. Lack of Fusion (a) Gas (b) and Keyhole (c) [44] ............................... 25 
Figure 7: Microscopy image of LOF Porosity, with characteristic un - melted powder 
present within pore, as well as irregular shape and relatively large size .................. 25 
Figure 8: Porosity Regimes for both Keyhole and Lack of Fusion porosity in metal 
AM components with respect to increasing scan speed [48] .................................... 26 
Figure 9: Computational ANSYS Simulation of Stress Simulation showing the Lack of 
Fusion pore acting as a stress concentrator [26]. ..................................................... 27 
Figure 10: Schematic of Gas Flow in general LPBF process chamber, depicting gas 
flow powder bed interactions [65] ............................................................................. 28 
Figure 11: Taxonomy of ML applications within the AM industry [33]. ...................... 30 
Figure 12:Process Structure Property (PSP) relation chain schematic in AM [33]. 
Text within boxes represents available data, while arrows and bold text represent 
examples of potential ML applications input and output data sources. .................... 31 
Figure 13: Schematic outlining input parameters for CNN model applied to LPBF 
production of Ti-6Al-4V. Input parameters include Thermal History from in-situ PM 
data (a) as well as process parameters indicated in (b). Output predicted distortion 
predicted in (c). CAMP-BD represent Convolutional and Artificial CNN applied to Big 
Data [44] ................................................................................................................... 32 
Figure 14: Exclusive (left) and Overlapping Clustering (right) example. In exclusive 
clustering, datapoints belong to one cluster only. In overlapping clustering, points 
may belong to two unique clusters. In probabilistic clustering, each datapoint is 
assigned a probability of belonging to a cluster, and then assigned to the cluster of 
highest probability [49] ............................................................................................. 33 
Figure 15: Procedure of implementation of Self Organising Map for Acoustic 
Emission analysis of Fused Filament Fabrication produced ABS by Wu et al. Feature 
extraction performed on in process acoustic emission signal, which is then used an 
input to SOM algorithm. Subsequently anomalous signals were detected. [59]. ...... 35 
Figure 16: An example of Binary Classification, where only two distinct clusters exist 
within the dataset [63] .............................................................................................. 37 
Figure 17: An example of Multiclass Classification, where multiple clusters exist 
within the dataset  [62] ............................................................................................. 37 

Figure 18: A case requiring Imbalanced Classification, as far more cases of the blue 
‘0’ class exist in comparison to the orange ‘1’ class [62] .......................................... 38 
Figure 19: Renishaw RenAM 500M LPBF System [23] ............................................ 43 
Figure 20: Photograph of a build plate, showing the cylindrical printed alloy parts. 
The 17 parts chosen for porosity analysis are marked by orange squares. ............. 44 
Figure 21: Schematic of the InfiniAM Spectral System [26] ...................................... 45 
Figure 22 An example of ImageJ porosity thresholding applied to a micrograph 
image (Left) of a Ti-6Al-4V produced on the Renishaw RenAM 500M. Based upon 
grayscale values of each pixel, each pixel in the micrograph is labelled as ‘Porous’ or 
‘Non-Porous’ (Right), and geometric features relating to each individual pore are 
calculated using the porosity analysis module available in ImageJ. The thresholded 
image contains porous point (In Black) and solid material (In White). Note that while 
the Bakelite mount surrounding the solid material is also black, this area was not 
included in porosity analysis. .................................................................................... 47 
Figure 23 VGStudios XCT Reconstruction of gas flow cylinder sample produced at 
same build plate location from high gas flow (36 per hour) (left); medium gas flow 
(31 per hour) (centre); and low gas flow (26 per hour) (right) ......................... 49 
Figure 24 Distribution of XCT Porosity across the build plates, based on 
measurements obtained from 17 samples examined for each of the three gas flow 
rate builds obtained from 17 samples examined for each of the three gas flow rate 
builds ........................................................................................................................ 50 
Figure 25: An example Cross Section Image taken from the Low Gas Flow build, 
demonstrating a considerable level of lack of fusion porosity ................................... 51 
Figure 26: Comparison between images of Ti-6Al-4V obtained using  XCT (a), and 
from cross sectional microscopy (magnification 275X) (b), for a sample printed at the 
low gas flow rate. Note the large ‘key-shape’ LOF pore, with an approximate length 
of 800 μm in the y-direction at point 1 on the XCT cross section (a), with the 
corresponding pore in the microscope image (b). .................................................... 51 
Figure 27: Covariance Constraint parameters for GMM plotted on open source ‘Iris’ 
data. Training datapoints marked with crosses, while test datapoints marked with 
dots. The GMM model was trained using the training dataset, while evaluated then 
upon the test set [121]. ............................................................................................. 57 
Figure 28: Two-dimensional feature space, with 6 points and resultant dendrogram. 
As can be seen from the dendrogram, no clear cluster number is evident. The largest 
vertical line (green) can be seen to intersect any of 4, 3 or 2 vertical lines depending 
on where the horizontal (red) line is placed [123] ..................................................... 58 
Figure 29: Hierarchical Clustering Dendrogram plots for (a) Low Gas Flow Rate 
(26 per hour) (b) Medium Gas Flow Rate (31 per hour) (c) High Gas Flow Rate 
(36 per hour) ....................................................................................................... 60 
Figure 30: Elbow plot comparison, with definite elbow point present (left), and no 
elbow point present (right). This lack of clear elbow in plot indicates that a new 
cluster number evaluation method required [48] ...................................................... 61 
Figure 31: Elbow Plots for XCT analysis of LPBF produced Ti-6Al-4V cylinders 
produced at: (a) Low Gas Flow Rate (26 per hour) (b) Medium Gas Flow Rate 
(31 per hour) (c) High Gas Flow Rate (36 per hour) ....................................... 63 

Figure 32: Low Gas Flow XCT data BIC values vs Cluster number for GMM 
clustering .................................................................................................................. 64 
Figure 33: Depiction of values used in silhouette score calculation [99]................... 65 
Figure 34: Silhouette scores for GMM plot with full covariance per cluster number for 
each data source. Each Data source containing three gas flow rates. Note that in (c) 
although the silhouette scores for a cluster number of 2 and 3 appear identical in the 
High and Medium gas flow, the value at a cluster number of 2 is marginally larger. 66 
Figure 35: GMM Results for XCT Analysis data from (a) Low (b) Medium (c) High 
Gas Flows. Total of 95489 Pores ............................................................................. 69 
Figure 36: GMM Results for Optical Microscopy Analysis data from (a) Low (b) 
Medium (c) High Gas Flows at Magnification of 275X. Total of 134987 Pores ......... 72 
Figure 37: GMM Results for Optical Microscopy Analysis data from (a) Low (b) 
Medium (c) High Gas Flows at Magnification of 624X. Total of 249,826 pores ........ 74 
Figure 38: Examples cross section images obtained from the two sample sets 
referred to in this chapter with the Gas Flow sample shown on the left and that 
obtained from the Test Set sample set, shown on the right ...................................... 79 
Figure 39: 5-Fold Cross Validation Example showing how the 20% of the total data 
(indicated in grey) acting as a test set, moves through each portion of the dataset 
[100] ......................................................................................................................... 80 
Figure 40: Example Confusion Matrix for a binary classification problem [101] ....... 81 
Figure 41: ROC Curves for 3 example models compared with flipping a coin. Better 
models are shown approaching the behaviour of a perfect classifier [101] .............. 82 
Figure 42: Gas/ Non-Gas Pore classification ROC Curve Test set. A higher ROC 
curve indicates a larger AUC score and consequently a more accurate classification.
 ................................................................................................................................. 87 
Figure 43: Lack of Fusion Pore classification ROC Curve Test set. A higher ROC 
curve indicates a larger AUC score and consequently a more accurate classification
 ................................................................................................................................. 89 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

LIST OF TABLES: 
 
Table 1: Examples of eight classification algorithms used in AM processes and their specific 
uses. ................................................................................................................................... 39 
Table 2: Chemical Composition (%wt) of Ti-6Al-4V ............................................................. 43 
Table 3: Processing Parameters used for the printing of the Ti-6Al-4V cylindrical parts. Note 
the printing studies were carried out three times, within which the Ar shielding gas flow was 
varied at three levels, as detailed in the text. ....................................................................... 44 
Table 4: Comparison between the porosity measurements obtained based XCT and 
Micrograph ImageJ Porosity Measurements. ...................................................................... 52 
Table 5: Cluster Average Feature Values across each Gas Flow for XCT data. Dark rows 
represent Irregular clusters, and light rows represent Regular clusters ............................... 70 
Table 6: Pore Type proportion at each gas flow in XCT data............................................... 70 
Table 7: Cluster Average Feature Values across each Gas Flow obtained from microscopy 
images (Magnification = 275X) ............................................................................................ 72 
Table 8: Pore Type proportion at each gas flow based on Optical Microscopy data 
(M=275X). Total of 55 Samples........................................................................................... 73 
Table 9: Cluster Average Feature Values across each Gas Flow for Optical Microscopy 
(Magnification = 624X) ........................................................................................................ 75 
Table 10: Pore Type proportion at each gas flow in micrograph data (M=624X). Total of 9 
Samples .............................................................................................................................. 76 
Table 11: Performance metrics for classifier algorithms applied to Gas Flow Set for 
Gas/Non-Gas Classification. Average Score in each metric presented for comparative 
purposes. The results are provided for the eight algorithms studied were: K-Nearest 
Neighbour (KNN); Decision Tree Classifiers (DTC); Naïve Bayes (NB); Support Vector 
Machine (SVM); Logistic Regression (LR); Multi-Layer Perceptron (MLP); Extreme Gradient 
Boosted Classification (XGB) and Gradient Boosted Classification (GB) ............................. 85 
Table 12: Performance metrics for classifier algorithms applied to Gas Flow set for 
Keyhole/Lack of Fusion Classification. Average Score in each metric presented for 
comparative purposes. ........................................................................................................ 85 
Table 13: Performance metrics for classifier algorithms applied to Test Set for Gas/Non-Gas 
Classification. Average Score in each metric presented for comparative purposes. ............ 86 
Table 14: Performance metrics for classifier algorithms applied to test set for Keyhole/Lack 
of Fusion Classification. Average Score in each metric presented for comparative purposes.
 ........................................................................................................................................... 88 
Table 15: Average metric scores for all eight classification algorithms in both 5-fold cross 
validation experiments upon the Gas Flow dataset. The values for the Gas/Non-Gas 
classification are noticeably larger....................................................................................... 91 
Table 16: Total proportion of both Regular and Irregular clusters at each gas flow within the 
Gas Flow dataset, based on GMM clustering ...................................................................... 95 
Table 17: Average metric scores for all eight classification algorithms in both 5-fold cross 
validation experiments upon the Gas Flow dataset. The values for the Gas/Non-Gas 
classification are noticeably larger....................................................................................... 95 
 
 
 
 

DECLARATION OF AUTHENTICITY

I hereby declare that this thesis is my own work and that it has not been submitted

anywhere for any award. I further declare that where other sources of information

have been used, they have been acknowledged by means of a comprehensive list of

references

ACKNOWLEDGEMENT

Firstly, I would like to thank my supervisor Professor Denis Dowling for giving me an

opportunity to pursue this MSc. I am grateful for his support, guidance, and expertise

provided throughout my studies.

I would like to thank all staff and students at UCD and I-Form with whom I have worked

with over these two years. I would like to thank Aoife Doyle, who was a great help

throughout the duration of this research. I would also like to thank Joan Kelly from

DCU for her help throughout the duration of this project.

Finally, I would like to thank my family, especially my father, mother, brothers Eoghan

and Niall, and sister Lucie whose support I am eternally grateful for.

CHAPTER 1: GENERAL INTRODUCTION

CHAPTER 1: GENERAL INTRODUCTION:

1.1 : INTRODUCTION:

Additive manufacturing (AM) is a materials processing technology with application in

a range of industry sectors, particularly for aerospace and medical device fabrication.

It is used both in the commercial production of final products, as well as in the rapid

production of prototypes. One of the most widely applied AM processes is Laser

Powder Bed Fusion (LPBF), which is a metal additive manufacturing technology used

in the production of complex metallic structures. Many end users of LPBF parts are for

high value added, precision parts used in components where failure would be critical.

As a result of this, understanding the causes of defects such as porosity, during LPBF

processing is of critical importance to AM equipment manufacturers. A deep

understanding of the causes of porosity, as well as an understanding of the different

forms of porosity is critical to achieve enhanced AM processing control. In this study

the use of machine learning techniques is investigated, as an approach to obtain a

quantitative estimation of the forms of porosity present in Ti-6Al-4V parts printed using

the LPBF process. This study evaluates both supervised and unsupervised machine

learning approaches, to evaluate and cluster porosity data obtained from the

examination of printed alloy parts.

1.2 : MOTIVATION:

LPBF is an area of increasing interest and is becoming more widely applied in the

production of precision engineering components such as orthopaedic devices used for

both hip and spinal devices. In order to assist the wider adoption of this technology

however a deeper understanding of the source of part defects, particularly porosity,

are important, due to their impact on the material and mechanical properties of the

printed alloy parts. To this end, an understanding of the forms of porosity present within

LPBF produced components is important, as the different types of porosity (lack of

fusion, keyhole and gas), each will have a different impact on a part’s mechanical

performance.

This MSc study aims to enhance the understanding of the types and distribution of

porosity present within alloy parts printed by LPBF. An assessment of porosity was

carried out using both X-Ray Computed Tomography (XCT) and Optical Microscopy.

The evaluation of the resulting porosity using statistical machine learning models was

investigated, using both unsupervised and supervised approaches. The aim is to gain

an understanding of pore morphology and its distribution in LPBF produced

components. To this end the application of statistical machine learning methods to

various forms of porosity analysis data will be implemented.

1.3 : PROBLEMS AND OBJECTIVES:

In additive manufacturing, ‘porosity’ can sometimes have a positive impact on device

performance, such as the large-scale porosity produced in biomedical lattice

structures. Other non-intentional pores are associated with microstructural pores

generated during alloy printing. These can be subdivided into three groups, namely

gas, keyhole, and lack of fusion porosity. These three microstructural forms of porosity

form due to a variety of different reasons during the LPBF process and have different

effects on the mechanical performance of the component. As such, it is of vital

importance that the distribution of these three classes of microstructural porosity are

understood, as well as the processing conditions which lead to their formation, within

the LPBF process. These three forms of microstructural porosity will be referred to as

‘porosity’ throughout the duration of this thesis. For many parts obtained using additive

manufacturing, post process treatments particularly hot isostatic pressing (HIP

Treatments), are routinely used to remove this type of porosity.

Within the LPBF process, chamber purging using Argon (Ar) gas is required in order

to prevent metal oxidation during powder melting. The flowing Ar gas also helps in the

removal of process by products, which are generated as the laser interacts with the

powder particles. This study firstly investigates the effect of Ar gas flow rate on the

porosity of the resulting alloy parts. To-date, there have been no reports in the

literature on the effect of systematically altering this inert gas flow rate, on the porosity

or other properties of printed alloy parts. This effect was investigated in this study by

printing Ti-6Al-4V cylinders in a production scale AM system (Renishaw RenAM

500M), at three different gas flow rates - 26 per hour (Low), 31 per hour

(Medium), and 36 per hour (High). Statistical machine learning algorithms were

applied to porosity data obtained from X-Ray Computed Tomography (CT), as well as

ImageJ Image analysis data which was obtained based on microscopy analysis of

cross sections of the printed cylinders. The overall objectives were to determine:

• Does alteration of the Ar purge gas flow result in a change in the overall porosity

of the Ti-6Al-4V parts?

• Does an increasing purging gas flow rate cause a proportionate increase in one

or more forms of porosity and if so, why?

• Does this increase in gas flow cause an increase in the number of ‘types or

clusters present within Ti-6Al-4V components?

• Does the porosity analysis technique (i.e. CT scanning or microscopy

examination), influence the sensitivity / accuracy of the porosity analysis?

• To obtain a comparison between the use of a range of unsupervised and

supervised machine learning algorithms for the determination of the type and

overall level of porosity within printed Ti-6Al-4V alloy parts. To determine if

these machine learning approaches accurate for the evaluation of porosity data

based on CT scans of alloy parts.

The aim of this thesis is to enhance the understanding of Ar gas flow rate during the

LPBF process, on the morphology and porosity of alloy parts printed. Three datasets

were used to evaluate the porosity type distribution with the Ti-6Al-4V alloy parts,

these were XCT analysis data, along with cross-sectional microscopy studies

(ImageJ), at two different magnifications. The advantages and limitations of the use of

supervised and unsupervised machine learning for the analysis of the alloy porosity

data were also evaluated.

In the case of the unsupervised machine learning, an approach known as clustering

is implemented. Clustering is a form of machine learning, whereby the model groups

the data into ‘clusters’ or groups, where each item in a cluster is more like items within

that cluster than items within other clusters. The objective is to determine if the use of

clustering approach can be used to evaluate the type and level of porosity present, for

cylinders printed at the three different Ar gas flow rates. This unsupervised machine

learning approach requires no user input, other than the number of expected clusters

within the dataset. This number can also be calculated through statistical means.

In the case of the supervised machine learning algorithms, the initial step is the

generation of a training dataset which consisted of a manually labelled subset of the

optical microscopy ImageJ geometric porosity data. The use of supervised

classification facilitates some user input into the performance of the algorithms. The

use of a manually labelled subset will enable the algorithms to ‘learn’ what the different

forms of porosity look like geometrically, and the use of classification algorithms with

labels enables the accuracy, among other metrics of the models to be assessed. Eight

different classification algorithms are assessed, and their performance compared. The

models to be used were K-Nearest Neighbour, Decision Tree Classification, Naïve

Bayes, Support Vector Machine, Multi-Layer Perceptron (Neural Network), Logistic

Regression, Gradient Boosted Classifier and Extreme Gradient Boosted Classifier.

These supervised approaches were selected as they are some of the most commonly

utilised supervised classification algorithms.

1.4: THESIS FORMAT:

This thesis is presented in six chapters: Introduction; Literature Review; Experimental

Methods and Materials; Cluster Number Evaluation and Unsupervised Machine

Learning; Supervised Machine Learning and Classification Evaluation; Conclusions.

Firstly, Chapter 1 introduces this MSc thesis, outlining the research questions and

motivations behind this thesis, as well as a general overview to the work undertaken

as part of this project.

Chapter 2 entails the literature review carried out as part of this study. The aim of this

review is to assess the current published literature and determine gaps within the

literature relevant to this project. This literature review is presented in two separate

sections. Firstly, a background on AM is presented, specifically laser powder bed

fusion, and the effect of process parameters including gas flow on porosity are

discussed. The effect of porosity on mechanical performance is also presented.

Secondly, a section on Machine Learning in AM is presented, with examples described

of previous applications of both Supervised, and Unsupervised Machine Learning

approaches. A discussion on the many applications and uses of Machine Learning

within Additive Manufacturing is also presented.

A discussion on the Experimental methods and Materials is presented in Chapter 3.

This section provides background on the LPBF printer used in this study, the Renishaw

RenAM 500M, as well as it’s associated in-process optical emission monitoring system

known as InfiniAM Spectral. Information on the alloy powder used, XCT Scanning

evaluation, cross-sectional evaluation and ImageJ image analysis are also included in

this section.

Chapter 4 discusses the comparison between the use of CT scanning and cross-

sectional microscopy for the evaluation of alloy porosity. The results of the porosity

measurements obtained using these techniques are presented and discussed.

Chapter 5 introduces unsupervised machine learning and discusses the various forms

of clustering investigated, in particular the Gaussian Mixture Model. The various

statistical methods used to determine the optimum cluster number are first described,

followed by the results of their implementation. Finally, the application of the Gaussian

Mixture Model to both XCT data, as well as micrograph data at two magnifications is

presented.

Chapter 6 provides an overview of the supervised machine learning approach,

followed by a discussion of the various analysis scores used in assessing a classifiers

performance. Two datasets are used in this study, both of which were obtained from

the micrograph analysis of Ti-6Al-4V. One set is referred to as the ‘Training Set’, while

the other dataset is known as the ‘Test Set’. A brief discussion of the two datasets is

presented. Finally, the assessment of the performance of the eight classifiers are

evaluated when applied to the two datasets.

Chapter 7 summarises the conclusions from this thesis. It includes a critical

assessment of the application of both unsupervised clustering techniques, as well as

supervised classification techniques when applied to the porosity data. This chapter

also contains a possible future works section.

Appendix A depicts the BIC Score graphs that were used in chapter 5 in an attempt to

determine the cluster number in each of the micrograph and XCT datasets. As each

micrograph dataset and the XCT dataset contained three gas flow rates, the BIC score

graphs are shown in a three-by-three grid.

CHAPTER 2: LITERATURE REVIEW:

2.1 OVERVIEW

This review firstly provides an overview of the importance of Additive Manufacturing,

with a particular focus on the Laser Powder Bed Fusion (LPBF) process, which is the

focus of this thesis. The effect of print defects, in particular porosity, are discussed,

highlighting how different types of porosity can impact differently on the performance

of the printed parts. The use of Machine Learning (ML) is then introduced and an

overview of this data analysis technique in process understanding is outlined, with a

particular emphasis on the use of unsupervised clustering techniques, as well as

supervised classification techniques. The application of ML clustering to porosity data

is then outlined, given its potential to categorise the type and level of porosity present.

2.2 Additive Manufacturing

Additive Manufacturing (AM) involves the printing of 3D computer models, printed

layer by layer until the final full 3-dimensional object has been manufactured [1]. These

3D computer models are obtained from Standard Triangle Language (.stl) files from

CAD software. The models may be constructed directly in CAD or imported into CAD

from topographical scanning methods such as Computed Tomography (CT) [2] or

Magnetic Resonance Imaging (MRI) [3]. The number of applications of AM is growing

rapidly as this printing technology becomes more mature.

There are a wide range of applications of AM in industry, in particular for geometrically

complex parts and individualised components, for which conventional manufacturing

approaches are both technically difficult as well as often very expensive. The medical

device sector is one example where the ability to produce rapid prototypes, high quality

bone implants, and accurate models of patients damaged bones for analysis are areas

unique to AM in this field [4]. AM printing now allows doctors to scan and build a model

of patient’s defective bone structure, which can provide them with a better idea of what

to expect before surgery and plan a more robust procedure saving time and cost, as

well as potentially improving the result a required surgery [4]. Bone implants also are

an area where AM has far exceeded the capabilities of other manufacturing methods.

AM methods allow for implants virtually identical in shape to the original bone, and due

to the ability of AM to produce incredibly precise small-scale geometries,

manufacturers can create lattice structures with controlled porosity in order to permit

osteoconductive bone ingrowth, an ability unique to AM [5]. The mechanical strength

obtained for the implanted devices have been reported to be up to three to five times

higher than implants produced through other manufacturing methods, while the

possibility of inflammation post-surgery caused by micro debris is reduced [6]. AM is

also a very beneficial technology for dentists, as it allows them to build a model of their

patient’s mouths, as well as to print dental implants [7].

AM also facilitates the production of lightweight components, which find application,

for example, in both the automotive and aerospace industries. For both industries, the

ideal component is as lightweight as can possible, exhibits similar or better mechanical

performance to conventional parts and of course does not compromise the safety of

the part [8]. Complex cross-sectional geometries such as the honeycomb cell are

feasible with AM technology, as well as a variety of other geometries that contain

cavities [8]. Part consolidation is also achieved with AM, enabling the production of

several components at once, reducing the amount of tooling, inspection required [9].

Figure 1: GE Aviation fuel injector nozzle for Superalloys. Metal AM facilitates the

production of more lightweight components in a single print process [10]

One of the advantages of AM is that it facilitates a considerably reduction in process

waste compared to traditional manufacturing methods [12]. Only material needed for

the component being printed is added to each layer (excluding supports where

necessary), compared to a process such as milling where material is removed from a

piece larger than the desired product until the desired product has been obtained.

Figure 1 depicts a fuel injector nozzle used in the Leaf engine [10]. For which use of

AM facilitated the production of the component in a single print process thus avoiding

the need to bond parts as well as achieving a significantly lighter final component

AM encompasses a wide range of individual processes, each process varying with

respect to machine technology and materials produced. Consequently, in 2012 the

American Society for Testing and Materials (ASTM) group "ASTM F42 – Additive

Manufacturing" defined a set of standards known as Designation: F2792 12A [63] that

classify a range of AM technologies into 7 distinct categories, and of these 2 are

predominantly used in the manufacturing of metal components, namely: Powder Bed

Fusion [13][14] and Directed Energy Deposition [15][16]. In this thesis the focus is on

one of the powder bed fusion technologies called Laser Powder Bed Fusion, for this

reason this is described in detail in the following section.

2.2.1 LASER POWDER BED FUSION

Figure 2: Cross Section Schematic of a Laser Powder Bed Fusion process at machine

scale (left) and powder scale (right) [45]

Laser Powder Bed Fusion (LPBF) is a form of selective laser melting, where a high-

power laser is used to melt select regions of metallic powder together in a layer-by-

layer process [45]. The goal of LPBF is to completely melt the feedstock powder in

order to obtain fully dense parts.

Figure 2 shows a cross section of an LPBF printer, consisting of a powder delivery

system, and an energy delivery system [45]. The powder delivery system is composed

of a powder delivery piston, which when raised supplies the build powder feedstock

material. The spreader then spreads the feedstock evenly across the build plate, which

is located over a fabrication piston. This piston lowers each time a layer is completed.

The energy delivery system is composed of either a laser (used in Selective Laser

Sintering (SLS), or an electron beam (used in Electron Beam Melting (EBM)), and a

scanner system composed of optical mirrors capable of focusing the beam to any point

on the build plate. Many LPBF systems come equipped with in-process monitoring

capabilities in order to facilitate the monitoring of parts in real time with the aim of

reducing the amount of rejected parts, save costs and improve reproducibility. Further

to the inclusion of in process monitoring systems, the implementation of closed loop

feedback systems, which automatically moderate process parameters in order to

improve part quality are of increasing interest in the LPBF industry [18][19].

A variety of in process monitoring systems have been developed for LPBF systems,

including image processing methods, thermal imaging, and melt pool spectroscopy

[20]. Amongst these the optical monitoring systems such as charged-coupled devices

(CCD’s) and complementary metal oxide semiconductor (CMOS) camera-based

systems, are common in industry. An aspect of this form of data monitoring is the non-

contact requirement with the powder bed, versatility and the large amount of data that

can be obtained [19]. Lu et al designed an optical process monitoring system for an

LPBF process, where an optical camera, a set of diode lights and a mirror were used

[21]. The density and tensile strength of the samples were then correlated with

‘features’ obtained from the camera images. This system then allowed mechanical

performance of the system to be calculated based upon the number of features

identified in the images.

An increasingly popular form of process monitoring involves the monitoring of melt

pool emissions and laser monitoring. Renishaw PLC have developed an in process

monitoring system known as the InfiniAM monitors both the laser, and the melt pool

across a wide spectral range [22][23]. The LaserVIEW system enables the intensity of

the laser input to be monitored up to a rate of 2 MHz, which enables any drift or

deviation in behaviour of the laser to be identified. This behaviour along with initial

system calibration information, enables the laser to be monitored over long periods of

time. The InfiniAM MeltVIEW module uses a dual coaxial diode system in order to

monitor emissions produced by the melt pool. A plasma diode records emissions in

the range [300 to 700nm], while the melt view diode monitors IR emissions in the range

[700 to 1700nm]. The Renishaw proprietary software InfiniAM Spectral then converts

this data into 2D and 3D representations as visual feedback for the user. There are

currently limited publications on the use of this process monitoring system, although

several studies by Egan et al., have demonstrated the technology’s ability to detect

larger porosity [39].

2.2.2 LPBF PROCESS PARAMETERS

Figure 3: Schematic depicting the laser beam and powder bed interaction [53]

LPBF contains numerous process parameters, which can influence the properties of

the printed part. Some of these parameters, are depicted in Figure 3, relate to the

beam, the powder, along with the scanning parameters [53]. The properties of the

powders such as morphology, particle size, shape, roughness and chemistry also

effect the performance of the printed part [23]. The scan strategy (describing the

motion of the laser in producing the part) also plays an important role in part property

performance, with scan strategies such as: parallel scanning; spiral scanning;

paintbrush scanning; and chessboard scanning, have all been demonstrated to impact

on mechanical properties [26][27].

A further factor influencing the LPBF process is the use of a controlled atmosphere in

the printing chamber using an inert gas, such as Nitrogen or Argon. This is in order to

maintain Oxygen levels below 500 parts per million [60]. The aim is to prevent the

metal powder from becoming oxidised or degrading during the printing process.

The parameters highlighted in yellow in Figure 4 indicate the process parameters that

have been reported to have the most significant impact on the generation of defects

during LPBF processing [61]. The highlighted process parameters can be related via

the Volumetric Energy Density (VED) equation [62]. VED expresses the amount of

energy imparted by the beam source into the powder bed, per unit volume. Assuming

100% of beam energy is used in melting the powder, this equation gives the amount

of energy used in melting 1 cubic millimetre of powder, as a function of laser power,

hatch distance, layer thickness and scan speed. The Volumetric Energy Density

equation is given in equation 1 [62]. The main benefit of using this equation is that it

can provide an indication of the process window for the LPBF process, where porosity

can be minimised, as seen in Figure 5 [63].

Figure 4: Process Parameters in LPBF (also known as SLM) with VED parameters

highlighted in yellow [63]

 

  

  

 Equ. 1

Where:

• v - Scan Speed The velocity at which the beam moves in each direction. Given

in units of 

• P - Laser Power SLM requires a high-power laser in order to fuse metallic

powders. Power typically ranges from 50W to 250W. Example lasers include

CO2 Lasers, Nd:YAG, Yb:YAG.

• h - Hatch Spacing The distance between adjacent beam track centres.

• δ - Layer Thickness The layer of thickness of the powder coating. This value

is generally quite thin at 20 - 50 µm [65]. This allows for high surface precision;

however, this comes at the expense of a slow build rate.

The VED equation generally exhibits two regimes, a high volumetric energy density

regime and a low volumetric energy density regime, both of which have been reported

to induce different types of porosity defects within AM alloy components [63]. These

defects are two different forms of porosity, known as Keyhole (KH) porosity in the high

VED regime, and Lack of Fusion (LOF) porosity in the low VED regime. These forms

of porosity are shown in the micrograph images inserted within the Porosity VED plot

in Figure 5:

Figure 5: Differing forms of Porosity formed at the VED values shown in LPBF

produced components. The insert images help to demonstrate the types of porosity

generated i.e. LOF (low VED) and KH (high VED). Minimised porosity in the

highlighted light blue region achieved through minimising both KH pores, and LOF

pores [63].

2.3 DEFECTS (INCLUDING POROSITY)

The microstructure, as well as the mechanical performance of the component

produced through AM can be affected by defects arising from process parameters

during manufacturing [34]. Additional parameters such as part orientation, support

structures, part design and material choice, can further impact the quality of the

produced component also [35]. Examples of defects include porosity, balling, hot

tearing, surface roughness, residual stress, and distortion due to the rapid solidification

of the metal powder in AM [36].

Residual stress can form due to high temperature differences between the molten

metal and cooler substrate [37]. This can lead to severe warping of the part, and in

some cases cracking. In order to avoid this the build plate is often heated, along with

the implementation of certain scan strategies such as spiral [38].

Balling is a defect whereby powdered material forms spheres wider than the parts

layer thickness. This defect can occur due to large oxygen content in the build chamber

(>0.1%). This defect can also form due to reduced scan speed with insufficient power

and can also be rectified through partial remelting of the powder [37][38].

Hot tearing is a defect that forms during the solidification of the melt pool. As this melt

pool solidifies, dendritic grains grow inward from the edge of the melt, and

consequently the centre of the molten material is the final region to solidify. As

opposing grains grow inward, a strain is placed on the molten metal and at the point

of solidification, this can result in cracks forming, known as hot tearing [39].

The average surface roughness of printed parts has been shown to be proportional to

the average feedstock powder particle diameter [40]. High levels of printed part

roughness can occur due to incorrect process parameters, or poor part design.

Insufficient energy being imparted into the powder also produces enhanced roughness

due to powder particles sticking to the surface of the part.

The focus of this research study is on the porosity generated in printed alloy parts and

as a result the following section provides details as to how it is generated, along with

the types of porosity. Porosity can be defined as the absence of material either within

a layer, between layers, or on the external surface of a part [41]. Porosity is generally

classified into three different classes [41]:

• Microstructural porosity, where porosity is formed unintentionally often due to

incorrect parameter choices leading to a substantial increase/decrease in VED.

• Structural porosity, which are intentional and intended to promote bone

ingrowth in orthopaedic components in the biomedical sector. This type of

porosity is often implemented through the creation of lattice structures in the

part.

• Functional porosity, which occurs due to de-binding between layers, and often

results in large, connected porosity.

Functional porosity can be minimised through the Hot Isostatic Pressing (HIP)

treatment of parts after printing [42]. In contrast, structural porosity is intentionally

produced. However, microstructural porosity must be minimised where possible as it

can significantly impact on a part’s mechanical performance [43]. Throughout the rest

of this study, microstructural porosity will be referred to as porosity. This porosity can

be further divided into three subclasses, namely [44]:

• Lack of Fusion (LOF) pores

• Keyhole (KH) Pores

• Gas (G) Pores

Figure 6: Microstructural pore type morphologies, generated with common (upward)

build direction. Lack of Fusion (a) Gas (b) and Keyhole (c) [44]

Each of the three classes has a unique formation mechanism, that can be related the

VED equation for AM processes, described earlier. The porosity regimes for all 3

microstructural pore types are plotted in Figure 8. Generally Keyhole and Lack of

Fusion porosity contribute to a significantly larger volume of porosity in comparison to

Gas porosity, resulting in an ideal process parameter ‘window’ existing between the

two regimes. This is shown in Figure 5, where porosity is minimised between 3.2 and

4.3  for LPBF produced metallic components. [41]

Lack of Fusion porosity occur when the VED is too low, possibly due to insufficient

Laser Power or a Scan Speed that is too fast. This causes insufficient fusion of the

metal powder, as less energy per cubic millimetre is being imparted into the powder

[45]. It results in irregular pore geometries, of varying sizes and sharper edges. LOF

porosity often contains un-melted powder particles within the pore itself, as seen in

Figure 7, a pore from this study.

Keyhole mode porosity however occurs when the VED is too large, because of

increased Laser Power or reduced Scan Speed. Consequently, this creates a vapour

depression within the melt pool, with high liquid flow velocity that closes in on itself as

Figure 7: Microscopy image of LOF

Porosity, with characteristic un -

melted powder present within pore,

as well as irregular shape and

relatively large size

the laser propagates forward [46]. This results in large rounded, but not perfectly

spherical pores, with a characteristic ‘J’ shape.

In the intermediary VED

range (blue region

highlighted in Figure 5)

both Lack of Fusion and

Keyhole type porosities are

minimised, as well as the

total porosity, as a result

[63]. However, minimal

amounts of small scale,

spherical porosity occurs,

which is Gas type porosity,

often known as

metallurgical porosity [47].

This has been attributed to

the gas entrapment of

shielding gas such as

Argon or Nitrogen, porosity

of powder particles, or alloy vapours within the melt pool.

2.3.1 MECHANICAL PERFORMANCE IMPACT OF POROSITY

The impact of porosity on the mechanical performance of LBPF components is

considerable, and there are a number of factors need to be considered when

discussing this impact. The first impact to consider, is the type of porosity, as it has

been demonstrated that keyhole and lack of fusion porosity has a significantly larger

impact on mechanical performance, compared to gas type porosity [49]. Both keyhole

pores and lack of fusion pores especially act as stress concentrators, due to their

irregular geometries. They can also act as initiation points for crack propagation within

the component [49]. The impact of Lack of Fusion porosity is so severe that processing

conditions for most alloys have been experimentally determined, in order to avoid

these pores [50][51][52]. The location of the pore within the component also influences

the specific mechanical property it will impact. It has been shown that pores located at

the surface, sub-surface, interior bulk material, interlayer, and at matrix interface will

affect corrosion, fatigue strength, stiffness, mechanical strength, and fracture

toughness of the component in particular [53].

Figure 8: Porosity Regimes for both Keyhole and Lack of

Fusion porosity in metal AM components with respect to

increasing scan speed [48]

In LPBF components,

porosity located on the

surface, sub-surface and

within the bulk of the material

has a considerable impact on

the strength and stiffness of

the part. Increasing the level

of porosity in LPBF printed

alloys reduces their yield

strength, ultimate strength,

and Young’s modulus under

both tension and loading

conditions [53]. Du Plessis et

al. concluded through a

combination of computational

simulation and experimental

verification that increased

levels of porosity in Ti-6Al-4V

components resulted in reduced yield strength and ductility [54]. Figure 9 shows an

example of a stress simulation from Du Plessis et al research. Regions of increased

irregularity, as well as pore edges, exhibit the most stress, and it has been established

in the literature that regions such as these usually initiate failure within components

[55]. Phutela et al. observed that LPBF produced Ti-6Al-4V samples with an increased

level of porosity exhibited reduced tensile strength, relative to identical samples with

low levels of porosity [55]. Al-Maharma et al demonstrated that more irregular pores

such as the Lack of Fusion pore depicted in Figure 9 caused a significantly more

detrimental impact on a components mechanical properties compared with that

obtained for pores with a regular geometry, such as gas and keyhole type porosity

[56]. It has been demonstrated in the literature that increasing levels of porosity in

metal alloys leads to a reduction in mechanical performance in a series of different

mechanical properties such as tensile strength, Youngs modulus, Poisson ratio

[57][58][59]. Therefore, it is paramount in AM processes to minimise the

microstructural porosity produced.

2.3.2 IMPACT OF LPBF GAS FLOW ON POROSITY

In LPBF processes, printing occurs under an inert atmosphere [60]. The term ‘inert’

refers to chemically inert or chemically inactive. Chemically inactive generally refers

to unreactive chemical gases which are often noble gases, or Nitrogen gas, and these

gases are important in the LPBF process as purging gases as the remove or ‘purge’

the environment of the printer of possibly reactive gases that may contaminate the

process through oxidation of the molten powder [61]. This inert gas flow is crucial to

the process as contamination of the process may result in altering the chemical or

physical properties of the printed component, possibly impacting the mechanical

properties or biocompatibility of the component [62]. It has been established within the

literature that gas glow plays a vital role in the LPBF process [60]. In Electron Beam

Melting (EBM) processes, in contrast to general LPBF processes, a vacuum is

Figure 9: Computational ANSYS Simulation of Stress

Simulation showing the Lack of Fusion pore acting as a

stress concentrator [26].

required in order to avoid interactions between the beam electrons and gaseous

molecules [63].

Figure 10: Schematic of Gas Flow in general LPBF process chamber, depicting gas

flow powder bed interactions [65]

While the inert gas flow prevents oxidation of the molten powder, the flow of gas also

plays an important secondary role in the removal of process emissions, such as

spatter from the molten melt pool, helping to create a clear path for the laser beam

through the powder bed unobstructed by process by products. Figure 10 shows a

general schematic of this process. It is important that the inert gas flow is homogenous,

as it has been demonstrated by Chen et al, that turbulence within the inert gas flow

can lead to undesired surface roughness within the produced component [32].

An aim of this current research is to assess the impact that purging gas flow has on

both the type and level of porosity in Ti-6Al-4V alloy components. Although it has been

well established in the literature that inert purging gas plays a vital role in the quality

of the produced component [62][63][64], a direct study on the impact of varying gas

flow on the overall level of porosity in printed alloy components, as well as a

relationship between inert gas flow and pore morphology, has not previously been

investigated.

2.4 MACHINE LEARNING IN ADDITIVE MANUFACTURING

The growing trend of automation with the emergence of ‘big data’ in industry is a

fundamental aspect of Industry 4.0. This term is used to help describe the current trend

of digitisation of manufacturing processes and has been defined as ‘automation and

data exchange in manufacturing technologies, including cyber-physical systems, the

Internet of Things, cloud computing and cognitive computing, as well as the creation

of the smart factory’ [66].

Machine Learning (ML), which is a subset of Artificial Intelligence (AI) has become

increasingly important approach for the handling of large volumes of process data

within Industry 4.0. ML is defined as ‘Computer Programming designed in order to

optimise performance criterion based on experience’ [33].

ML can be divided into three main categories, namely supervised learning,

unsupervised learning, and reinforcement learning [34]. In supervised learning, each

item, consists of an input and output. The output ‘Y’ can be either a continuous or

categorical variable, whereas the input vector ‘X’ is a vector containing all features all

involved features in the form ( , , , , …., ), where N is the number of

features within the dataset [33]. Depending on whether the output ‘Y’ is a continuous

or categorical variable, two different forms of supervised learning can be used. In the

case of a categorical variable, Classification methods can be used, such as indicating

whether a part is porous or non-porous. If the output ‘Y’ is a continuous variable

Regression models can then be used. However sometimes input data does not have

an output label, and in this case unsupervised ML models are implemented. These

models instead infer meaning from the unlabelled data structure. Typical applications

of unsupervised learning involve Clustering methods, where input items are grouped

together based upon their similarity [34]. Another application of unsupervised methods

is anomaly detection, where anomalous input items are detected, relative to the input

dataset. Reinforcement learning, or semi-Supervised learning involves the model in

question interacting with its environment, and ‘learning’ to take the best course of

actions in order yield the greatest reward [35]. This approach does not require a

training set and learns from its own actions. Reinforcement learning is the type of ML

implemented in self driving cars [36].

AM technologies produce vast amounts of build data relative to other manufacturing

technologies, this has the potential through the application of machine learning tools,

to optimise the AM process at nearly every stage in the workflow [70]. A taxonomy of

ML applications within the AM industry is presented in Figure 11.

The application of ML to AM has ranged from optimising process parameters to

anomaly detection based on the analysis of in-situ process monitoring data [33]. A

major issue for the wider adoption of AM is the difficulty in achieving consistent part

quality, due to process defects such as porosity. Part quality is highly dependent on

process parameters based on those in the VED equation 1, in section 2.2.2. The

relationship between these process Parameters, to the produced Structure, and

consequently the Properties (PSP) have been discussed and reviewed in several

publications [37][38]. One method to ensure part quality and consistency is the

application of in process monitoring systems, however these systems require an

efficient defect detection system. Egan et al. implemented a statistical anomaly

detection algorithm known as the Generalised Extreme Studentized Deviate (GESD)

test, that was successfully applied post-process to in situ process monitoring data to

detect a wiper tear within the produced lattice structure [39]. Another method to

understand these PSP relations is through a series of experiments with the aim of

varying these process parameters in order to assess their impact upon component

properties. This can however prove both costly and time consuming.

2.4.1 ML APPLICATIONS IN AM

Figure 11: Taxonomy of ML applications within the AM industry [33].

Some current applications of Machine Learning within the Additive Manufacturing

industry are shown in Figure 11. The multitude of possible data sources lends itself

towards a variety of possible ML applications. Some combinations of these data

sources have been studied extensively, and are written in bold in Figure 12, and shall

be discussed further in the following sections.

Figure 12:Process Structure Property (PSP) relation chain schematic in AM [33]. Text

within boxes represents available data, while arrows and bold text represent examples

of potential ML applications input and output data sources.

2.4.1.1 DEFECT DETECTION, CLOSED-LOOP CONTROL AND

QUALITY PREDICTION

Recent advancements in the use of in-situ process monitoring systems have enabled

many different AM technologies to capture real-time data, that should enable defect

detection [42]. There are several ways in which ML models can be applied to this real-

time data, which can include images from a CCD camera source, thermal emission

data, as well as post process XCT scans of the components. One possible application

of ML to this data would be the use of unsupervised clustering to the data, whereby in

process monitoring data can be grouped into cluster that display regular, and irregular

behaviour, acting as a pseudo-anomaly detection algorithm in order to detect defects

[42]. A more time-consuming ML application to investigate of in-process data, involves

manually labelling the data, through XCT scan data, as either Defect or Non-Defect.

This labelling can be obtained through experimental results, or knowledge of the

defects present within the in-process data. This labelled data can then be used an

input to a supervised classification algorithm, which would then class every instance

of the data as defect/non-defect. A third method involves real time training of a

supervised regression model, where a random variation in one of the input features

‘’ is compensated for by a variation of the output label ‘Y’. Wang et al implemented

one of these real times learning regression models in a Material Jetting (MJ) process

[43]. In order to extract droplet features, image analysis of CCD camera images was

conducted, in order to extract four features, namely length, volume, speed and

satellite. The drive voltage used to stabilise the droplet was the continuous target label,

and through real time learning implemented in a convolutional neural network (CNN),

stochastic variations in input features were then compensated for by varying the drive

voltage value. It was shown that the process achieved increased stabilisation in droplet

behaviour.

2.4.1.2 GEOMETRIC ACCURACY ANALYSIS AND CONTROL

Common manifestations of defects in AM printed parts, include part distortion, as well

as porosity, along with a reduced surface quality, and geometric inaccuracies [43].

These may impinge upon the usability of AM in precision engineering applications,

such as in the aerospace, and the orthodontics sectors, where extremely tight part

tolerances are required [44]. To this end, ML algorithms have been implemented in

order to predict geometric inaccuracies, quantify this geometric deviation and

subsequently compensate for this deviation during the design of the part being

printing. Francis et al implemented this framework through a Convolutional Neural

Network model, applied to the LPBF process, which is indicated schematically in

Figure 13 [44].

Figure 13: Schematic outlining input parameters for CNN model applied to LPBF

production of Ti-6Al-4V. Input parameters include Thermal History from in-situ PM data

(a) as well as process parameters indicated in (b). Output predicted distortion

predicted in (c). CAMP-BD represent Convolutional and Artificial CNN applied to Big

Data [44]

The thermal history obtained through in-process monitoring data, in combination with

the process parameters of the system were used as inputs, and the distortion of the

part, obtained through XCT scanning was used as a continuous label for the CNN

model. The CNN model was then trained in order to predict distortion, which is then

reverse imported into the CAD model in order to compensate for the predicted error.

By this method, the accuracy of prints was significantly improved.

2.4.2 UNSUPERVISED CLUSTERING

In unsupervised ML, the data is unlabelled, such that each row vector contains a vector

of the form (, , , , …., ) with no output or ‘label’ [45]. As such, many

unsupervised algorithms’ main purpose is to uncover hidden patterns within the data,

or to group similar data together. One of the most common types of unsupervised

algorithms is this grouping, which is known as Clustering. In Clustering analysis, data

is separated into different numbers of groups based upon their similarity such that

objects in the same group are more like each other than they are to other groups.

Clustering can general be classified into two different types, either ‘exclusive’ or

‘overlapping’ clustering [45]. In hard clustering, datapoints can only belong to one

cluster, whereas in soft clustering they are assigned based upon the likelihood of them

belonging to a certain cluster. A schematic showing both a scenario of exclusive

clustering, and of overlapping clustering is presented in Figure 14.

Figure 14: Exclusive (left) and Overlapping Clustering (right) example. In exclusive

clustering, datapoints belong to one cluster only. In overlapping clustering, points may

belong to two unique clusters. In probabilistic clustering, each datapoint is assigned a

probability of belonging to a cluster, and then assigned to the cluster of highest

probability [49]

A plethora of clustering algorithms exist, and these algorithms differ from each other

based upon how they cluster data points. These different models, as well as being

‘exclusive’ or ‘overlapping’ clustering, can be classified into connectivity models,

centroid models, and distribution models [46][47][48]. Each of these types of models

have their own advantages and disadvantages.

The clustering sub-group Connectivity models are based upon the principal that

datapoints closer to each other are more like each other, than datapoints further away

from each other. An example of Connectivity clustering would be the Hierarchical

Clustering method, which uses distance-based metrics in order to calculate similarity

within the data [50]. Distance here, refers to how close each datapoint lies to another

within a unitised feature space. These distance-based metrics include Euclidean,

Manhattan, and Mahalanobis distance, and each vary depending on the how they

measure distance mathematically [50]. These models either follow a bottom-up

approach, where each datapoint is initially an independent cluster, and merged later

using a distance measure, or a top-down approach, where all datapoints initially

belong to one cluster, which is then split recursively through some distance measure.

The principal advantage of Hierarchical Clustering is that clustering results are

presented graphically in a ‘dendrogram’. This shows the number of clusters present

within the data at every possible distance [51]. This then informs the user the optimum

number of clusters present within the dataset. The number of vertical lines intersected

by a horizontal line, placed in the interval of the largest distance between successive

clusters is the optimal value for the number of clusters.

The centroid model clustering sub-group, similarly, to connectivity models uses

distance-based metrics, however these distances are measured between each point

and their respective cluster centroid rather than to other datapoints [53]. An example

of Centroid clustering is ‘K-Means Clustering’, one of the most widely used clustering

methods [53]. The ‘K’ in K-Means stands for the number of clusters within the model

and must be defined before implementing the model. Generally, dendrograms or

‘elbow plots’ can be used to infer the number of clusters present within a dataset.

The third form of Clustering, Distribution model clustering operates through assessing

certain probability criteria (dependant on the specific distribution clustering model in

question) and assigning points to the cluster with maximum probability [54]. One of the

most popular Distribution models is the Gaussian Mixture Model (GMM), and this

model uses the famous ‘normal’, or Gaussian Distribution to model each cluster. The

normal distribution describes the bell-shaped curve that contains as many points larger

than its mean as smaller than it, with the mean, median and mode all being equivalent.

The GMM uses probabilistic models which assumes a certain number of Gaussian

distributions, and each of these distributions represents a cluster [55]. The Gaussian

distribution, also known as the normal distribution, is usually represented in a bell-

shaped curve, where the assumption is that the dataset has an equal number of

measurements above and below the average (mean) value. If a particular distribution

is deemed ‘normal’, it will share the same mean, median and mode value [55]. While

k-means only considers the mean when determining a cluster centroid, in addition to

the mean, the GMM also considers the variance of the data [56]. The GMM model will

be applied in this research study, in order to investigate the effect of gas flow on pore

morphology in LPBF manufactured Ti-6Al-4V.

2.4.2.1: UNSUPERVISED CLUSTERING APPLICATIONS IN AM

There have been several reports of applications of Clustering within AM reported in

the literature, as discussed in this section. A Clustering algorithm that has been

frequently used in research is the Self Organising Map (SOM), which is a form of

neural network developed for unsupervised learning. Khanzadeh et al implemented

an SOM model in their investigation of a geometric inaccuracy [57]. A large dataset

containing the geometric inaccuracies of various processing parameters was

assessed, and clustered. This study concluded that the more clusters a particular set

of processing parameters produced, the more type of geometric deviations it produced

in terms of magnitude and direction.

Another study by Khanzandeh et al. applied SOM in the detection of defects in Ti-6Al-

4V, produced through DED [58]. This study involved anomaly detection within melt

pools through unsupervised clustering, and was predicated upon two assumptions:

Firstly, that an abnormal melt pool has no correlation with other melt pools; and

secondly, that the number of abnormal melt pools is far outnumbered by the number

of optimal melt pools. The melt pool temperature data was therefore clustered, and

the clusters with little correlation to other clusters were considered anomalous, and it

was found that porosity tended to form at these anomalous melt pool locations. Wu et

all also implemented SOM in the anomaly detection of abnormal acoustic emission

(AE) signals from fused filament fabrication (FFF) printed acrylonitrile butadiene

styrene (ABS) [59]. Initial feature extraction of the AE signal waveform was

implemented, prior to the SOM Clustering, and it was found that the anomalous AE

signals could be successfully detected using SOM, and that they corresponded to

polymer samples (ABS), that experienced failure mechanisms during printing such as

shrinkage, distortion, or scratching. Figure 15 depicts the procedure implemented by

Wu et al.

Figure 15: Procedure of implementation of Self Organising Map for Acoustic Emission

analysis of Fused Filament Fabrication produced ABS by Wu et al. Feature extraction

performed on in process acoustic emission signal, which is then used an input to SOM

algorithm. Subsequently anomalous signals were detected. [59].

Zhao et al used GMM and k-means techniques for the classification of in-situ thermal

imaging data obtained during the printing of Ti-6Al-4V parts by Direct Energy

Deposition [60]. The clustering models were used to identify defective melt pools in

this additive manufacturing process, which was then verified using XCT. It was found

that morphological melt pool features alone were incapable of identifying anomalies,

and that the thermal imaging features could potentially increase accurate anomaly

detection. Due to the GMM models’ ability to identify a combination of multi-

dimensional Gaussian probability distributions, it has the potential for the examination

of XCT porosity data. Snell et al applied K-Means clustering to XCT of a variety of

alloys produced through LPBF and found that this method of pore evaluation to be

much improved on traditional statistical optimisation methods such as defined class

limits with boundary optimisation [20]. Both methods predicted similar quantities of

Lack of Fusion pores (186 and 183 for K-Means and Boundary Optimisation

respectively) however a considerable difference in Keyhole pores was reported (373

and 1 for K-Means and Boundary Optimisation respectively). The difference in Keyhole

mode pores could possibly be due to incorrect initial boundary value selection for the

Boundary Optimisation method. The majority of clustering until now has been applied

as a form of anomaly detection, particularly common is the implementation of

clustering applied to discretised melt pool emissions, for the purpose of relating in

process data to the final printed parts [42].

2.4.3 SUPERVISED CLASSIFICATION

Supervised learning is the most widely applied ML technique within AM processing,

as it assists in addressing the problem of predicting a class or variable [33]. The

difference between supervised and unsupervised is that in supervised learning, the

data is labelled, such that each input vector of N features is of the form (, , ,

, …., , Y), where Y is the ‘label’ of that vector. The nature of this label determines

the type of ML model that is used, where a continuous label implies a regression

model, and a categorical label implies a classification model. In classification

problems, the model can be trained on the training set to make classifications and use

this training to classify new inputs.

Classification models make use of the training dataset in order to approximate a

mapping function ‘f’, that can take an unseen input vector  and map it using the

approximated mapping function to a discrete output variable Y. Classification models

can generally be classified as either ‘lazy’ or ‘eager’ learners [61]. Lazy learners store

the training data, and classify new cases based upon the most similar data in the

training set. Lazy learners include models such as K-Nearest neighbour models. In

comparison with eager learners, lazy learners have reduced training time, with

increased prediction time. Eager learners in comparison construct a classification

model based on the training data, before receiving test data. Due to this construction,

eager learners exhibit the opposite behaviour to lazy learners, in that they have an

increased training time and reduced prediction time. Eager learners include Support

Vector Machines, and Neural Network models [61].

There are four possible types of classification tasks in supervised classification,

namely: Binary Classification; Multiclass Classification; Multilabel Classification; and

Imbalanced Classification [62]. Binary Classification, as the name implies involves

problems where only two class labels exist. An example binary classification problem

is classifying email spam as either spam or non-spam. In binary classification

problems, many class labels are in string format, e.g., ‘Cancer/non-Cancer’,

’Spam/non-Spam’. Therefore, many classification algorithms contain auto encoders

that convert these classes into positive and negative numeric labels 0 and 1. In binary

classification, it is common for many models to incorporate a Bernoulli distribution in

their mapping function [62]. This distribution is a discrete probability distribution that

predicts the probability ‘p’ of a test vector  belonging to a class 1 [62]. The 0 class

then has a probability of (1-p). Some models are specifically designed for binary

classification such as Logistic Regression, and Support Vector Machines. A simple

example of binary classification is shown in Figure 16, where the input features are

simply X and Y grid coordinates, facilitating the classification of points into distinct

clusters [63].

Figure 16: An example of Binary Classification, where only two distinct clusters exist

within the dataset [63]

Figure 17: An example of Multiclass Classification, where multiple clusters exist within

the dataset [62]

Multiclass classification in contrast to binary classification, is where more than one

possible class label exists [62]. An example of multiclass classification is facial

recognition on a smartphone, or plant species classification as a variety of possible

faces or plants may need to be identified by the classifier. A common practise is to

model a multi class classification task with a model that can predict a Multinoulli

probability distribution [62]. This distribution is a discrete probability distribution that

covers cases where an event can have a categorical outcome, such as K in {0,1, 2, …

K}. In classification tasks the model predicts the probability that a test example belongs

to each of the classes. Many algorithms that can be implemented in binary

classification can also be implemented in multiclass classification. Figure 17 shows a

scenario in which a distinct number of clusters are present, similar to the situation in

Figure 16. However, in this case multiclass classification is required, as there are more

than two clusters.

Multilabel classification is a situation where two or more class labels, where each item

may contain one or more labels. This is especially prevalent in image recognition,

where an image may contain labels such as ‘dog’, ‘tree’, and ‘person’. In these

problems, it is common to use models that can predict multiple outputs containing the

permutations of possible label combinations, with each output often containing a

Bernoulli probability distribution, essentially a model that implements a series of binary

classification predictions. Specialised models such as Multilabel Random Forest, and

Multilabel Decision Trees exist for this situation [62]. Imbalanced Classification refers

to cases in which the number of items in one class far exceeds the other class. This

is typically seen in binary classification problems, such as in fraud detection, anomaly

detection, and in medical diagnostic testing [62]. In order to compensate for this

imbalance, sometimes up sampling of the minority class is performed, or down

sampling of the majority class. Specialised imbalance algorithms also exist, that are

especially sensitive to the minority class, such as Cost-sensitive Logistic Regression

models, or cost-Sensitive Support Vector Machines. Figure 18 depicts a case where

Imbalanced Classification models would be necessary, due to the number of ‘0’ items

far exceeding the number of ‘1’ items.

Figure 18: A case requiring Imbalanced Classification, as far more cases of the blue

‘0’ class exists, in comparison to the orange ‘1’ class [62]

There is area a variety of classification algorithms that have been already applied in

AM technologies. The choice of algorithm depends on the type of data that is being

used, as well as the computation power available, as some algorithms are more

intensive than others [96]. Summarised in table 1 are several classification algorithms,

as well as their use in AM.

Both, Gradient Boosting and Extreme Gradient Boosting algorithms have become

increasingly popular in recent times [97]. Extreme Gradient Boosting in particular has

become one the most frequently used models in machine learning competitions and

is regularly the best performing model in these competitions [97].

Classification

Algorithm

Input

Output

Use

K-Nearest

Neighbour

Melt pool

characteristics

Porous or non-

Porous LPBF

components

Defect Detection

[98]

Support

Vector

Machine

Spectral Intensity

Graph

Defect detection in

Direct Metal

Deposition

Defect Detection

[99]

Naïve Bayes

Dimensional Variation

in LPBF components

Types of infill

Quality

Assessment [100]

Decision Tree

Classifier

Process Parameters

Surface Roughness

Quality

Assessment [101]

Multi-Layer

Perceptron

In-situ images

Defect Detection in

LPBF produced Ti-

6Al-4V

Defect Detection

[102]

Logistic

Regression

Process Parameters

Process parameter

optimisation for fully

dense components

Quality

Assessment [103]

Gradient

Boosted

Classification

Thermal Imaging data

Melt pool defect

detection in DED

produced metallic

alloys

Defect Detection

[104]

Extreme

Gradient

Boosted

Classification

Process Parameters

Distortion

prediction in

metallic alloy

components

Process parameter

optimisation [105]

Table 1: Examples of eight classification algorithms used in AM processes and their

specific uses.

2.4.3.1: SUPERVISED CLASSIFICATION APPLICATIONS IN AM

There are a wide range of possible applications for ML in AM technologies, specifically

supervised classification tasks. Some of the most applied techniques involve Decision

Trees (DT), Support Vector Machines (SVM), and Convolutional Neural Networks

(CNN).

One of the main reasons for the increased use of DT models in AM is their

interpretability in comparison to other ML techniques [63]. Khandadeh et al applied

Principal Component Analysis (PCA) to thermal imaging in situ data of DED produced

Ti-6Al-4V. This data was then either labelled as porous, or non-porous which was then

labelled as through XCT scanning of the components [63]. A series of supervised

classifiers were applied to this data, and DT showed consistent above average

performance. Although DT are a relatively simplistic model, they tend to perform well,

and serve as a good comparison model to more complicated classifiers.

The SVM model is one of the most common classifier models in AM [64][65][66] and

is used in binary classification problems. Each input output combination contains an

N dimensional input vector (where N is the number of input features) and its output

plotted in an N dimensional feature space. SVM then produces a hyperplane in that

feature space in order to partition the two groups. The choice of Kernel in SVM plays

an important part in the overall accuracy of the model, with some complex kernels

yielding an increased accuracy but increasing computation time. Zhang et al

implemented SVM for defect detection in in situ images, yielding 90.1% accuracy in

DED produced Ti-6Al-4V [65]. This approach was validated using XCT scans to

validate the SVM results.

The most popular classification method in AM is the Neural Network (NN) model [63].

Regular NN models such as Multi-Layer Perceptron (MLP) are sufficient when the

problem consists of parameters and classes, specialised NN models known as

Convolutional Neural Networks (CNN) are used for image-based problems. Scime et

al implemented a CNN model for defect detection in in situ images produced from

LPBF produced Ti-6Al-4V, and found defect detection, and defect differentiation

accuracies of 97% and 85% respectively [63].

Overall NN models are complex but perform strongly in most classification tasks [63].

While the choice of models used in classification should be based upon input features,

and computational intensity. Most classification models can be used in parametric

classification problems, however for image analysis or AE emission problems CNN

and SVM models are suggested. In this thesis, several classification algorithms will be

applied to tabular porosity data obtained from cross sectional microscopy images

examined using ImageJ software.

The application of supervised ML algorithms in AM has been predominantly oriented

around process parameter optimisation, or property prediction in AM components.

This thesis aims to use supervised classification to differentiate between image

analysis porosity data for a series of AM components produced at varying gas flows.

The area of supervised classification applied to image analysis data of porosity in AM

is the first to be investigated, to the authors knowledge. In general, in ML studies, it is

best to implement a series of classification models, and to assess their performance,

rather than optimising a single model.

2.5 LITERATURE REVIEW SUMMARY

This review in addition to providing an overview of AM, demonstrated the enhanced

capabilities of the technology when compared to traditional manufacturing techniques.

The differing types of AM processes are introduced, as well as a detailed discussion

regarding the areas and industries that AM has had its most considerable impact. Due

to their relevance to the research work the focus was on the LPBF process, with

particular attention to the powder bed laser interaction. The effect of individual process

parameters, and their relation to the formation of different types of defects, particularly

porosity was detailed. The effects of different levels and types of porosity, were

discussed along with their effect on the mechanical performance of the resultant alloy

parts. Although a number of authors have suggested the importance of inert gas flow

inside the chamber to the quality of the LPBF part, the direct influence of the gas flow

on the porosity of the part has to-date not been investigated, in detail. In this thesis

the impact of systematically altering the flow rate of the purge gas during the LPBF

printing of Ti-6Al-4V cylinders is explored, to evaluate how the gas flow rate influences

either the type or level of porosity in printed alloy parts. This study will also compare

the use of XCT and optical microscopy cross sectional analysis, as approaches for

investigating alloy porosity.

This literature study included an in-depth review of Machine Learning in general, along

with its specific applications to AM. This included the use of both Unsupervised

Machine Learning, specifically Clustering, in addition to the application of Supervised

Machine Learning, specifically Classification. The different forms of algorithms applied

in ML are discussed, as well as examples of where they are applied. The emergence

of ML as a vital statistical tool in the optimisation of AM is described.

Both the use of unsupervised and supervised machine learning are investigated in this

thesis for the analysis of porosity data. In the case of the latter, eight different

supervised classification algorithms are applied to micrograph data, with the aim of

evaluating algorithm performance, and ability to differentiate between the three types

of porosity. To this end, it is the first application of unsupervised clustering to XCT and

micrograph porosity data, as is the use of supervised classification to differentiate

types of porosity within an alloy matrix.

CHAPTER 3: EXPERIMENTAL METHODS AND MATERIALS

3.1 INTRODUCTION

This chapter provides an overview of the printing of the Ti-6Al-4V alloy used within this

porosity study. Details of the Renishaw RenAM 500M LPBF system used to print the

parts, along with it’s in-process photodiode monitoring system, known as InfiniAM are

also provided. The characterisation of porosity in the alloys is also discussed, using

both X-Ray computed tomography, along with the optical microscopy analysis of the

sectioned Ti-6Al-4V alloy samples. ImageJ was used in-turn for the analysis of the

resulting optical microscopy images.

3.2 MATERIALS: TI-6AL-4V

Gas atomised Ti-6Al-4V, was sourced from AP&C (GE Additive, Montréal Canada)

and was used for the manufacture of alloy test samples by LPBF. This material has a

mean powder particle size of 34 μm, with a quoted size distribution in the range 20 –

46 μm. Powder size is controlled through a sieving process, internal to the Renishaw

system. This removes powder above 32 μm. The powdered material has a

composition according to ASTM F3001 and is shown in Table 2, as per the AP&C test

certificate [22].

Other

Bal.

6.34

3.81

0.019

0.13

0.03

<0.01

0.002

<0.01

<0.04

Table 2: Chemical Composition (%wt) of Ti-6Al-4V

3.3 RENISHAW RENAM 500M AND INFINIAM IN- PROCESS MONITORING SYSTEM

The LPBF RenAM 500M is a production scale AM printing system (Renishaw PLC,

United Kingdom), utilises a Yb: YAG fibre laser system, which operates in a modulated

mode [39]. The laser has a maximum power output of 500 W, at a wavelength of 1070

nm. The system has a maximum operational build volume of 250 mm x 250 mm x 335

mm. For the manufacture of Ti-6Al-4V, argon gas is used both to provide an inert

atmosphere as well to remove process by-products. A vacuum is first applied to the

build chamber reduce oxygen within the chamber to a level of 0.6%, once this level is

achieved argon is backfilled into the chamber to provide an inert atmosphere during

part printing.

Figure 19: Renishaw RenAM 500M LPBF System [23]

In order to investigate the effects of Ar gas flow on the porosity of the printed alloy

parts, the laser power, laser speed parameters etc., were kept, while the Argon gas

flow purging rate was varied. This was set at three different values namely Low

(26per hour), Medium (31per hour) and High (36per hour). Each build

contained 77 cylinders produced at the same locations within the build plate. For each

build, cylindrical Ti-6Al-4V specimens with a height of 25 mm and a diameter of 15

mm were printed, under the processing conditions given in Table 3. Seventy-seven

cylinders were printed at each of the three gas flow rates investigated. Seventeen

samples were selected from each print build for XCT porosity analysis, in order to

obtain a representative distribution across the three build plates. The test parts were

selected from the same print plate position for each build, as indicated in Figure 20.

The specimens were removed from the build-plate using wire EDM.

Scan Type

Laser

Power

(W)

Point

Distance

(µm)

Exposure

Time (µs)

Hatch

Distance

(µm)

Layer

Height

(µm)

Hatch

200

Border

160

Contour

200

Table 3: Processing Parameters used for the printing of the Ti-6Al-4V cylindrical parts.

Note the printing studies were carried out three times, within which the Ar shielding

gas flow was varied at three levels, as detailed in the text.

Figure 20: Photograph of a build plate, showing the cylindrical printed alloy parts.

The 17 parts chosen for porosity analysis are marked by orange squares.

A second sample set, which is referred to in Chapter 6 as the ‘Test Set’ was obtained

from a separate Ti-6Al-4V alloy printing study, which was carried out using the

Renishaw RenAM 500M system. This sample set was produced using the same

processing parameters as described in Table 3. The produced samples were

cylindrically shaped, with diameters of 10mm and a height of 50mm.

3.3.1 IN-PROCESS MONITORING

The Renishaw RenAM 500M LPBF system comes equipped with an inbuilt photodiode

based process monitoring system known as the InfiniAM Spectral system. A schematic

of this system is shown in Figure 21 [26].

Figure 21: Schematic of the InfiniAM Spectral System, the meltpool data labelled 18

is monitored using the photodiodes labelled 4 and 5 [26]

In Figure 21, a 500 W ytterbium laser emits light with a wavelength of approximately

1070 nm, as seen in label 1. A fraction of the laser passes through a fixed mirror and

is detected in the LaserVIEW module, at label 10, which records information about the

laser input energy at a rate of 100 kHz. Emitted radiation from the meltpool, labels 13,

15, 18, is transmitted back up the laser path, where it is ultimately recorded by two

photodiodes at a rate of 100kHz, at labels 4 and 5. The photodiodes make up the

MeltVIEW system, where one photodiode 4 records visible light emissions, and the

second labelled 5, measures thermal, infrared (IR) emissions. In total, there are three

photodiode sensors, at labels 4, 5, 10.

3.4 X-RAY COMPUTED TOMOGRAPHY

The porosity of the printed cylindrical parts was evaluated using X-Ray Computed

Tomography (XCT) using a GE Nanotom M system, which has a resolution of 12.5

μm [27]. The XCT scans were analyzed using the porosity/inclusion analysis (PIA)

module in VGStudio Max version 3.5 [37]. Datos Rec Software reconstructs images

taken by XCT, while VGStudio Max imports these XCT volumes and displays the

reconstructed component as a 3D model. The surface determination tool allows for

the program to identify the material/air boundary by measuring the grey values of

individual ‘voxels’, or 3-dimensional pixels. The PIA module examines the grey value

of each voxel within the 3D model, to check if it is a part of a pore/void, and a group

of related voxels is allocated to be a part of the same pore. A region of interest was

created for analyses, which spanned from 23 to 24 mm. The selected region avoided

variations between parts caused by the engraved labels which had been placed on

the top surface of the parts, as well as any damage associated with the use of wire

EDM, to remove the parts from the build plate. A Porosity Inclusion Analysis (PIA)

module VG Easy Pore was applied to the parts using a minimum filter volume of 60,

to minimize the effect of noise from the XCT scan data being labelled as porosity.

The VGStudio MAX PIA module outputs a list of features relating to each individually

identified pore. The features diameter, voxel volume, surface area, sphericity,

compactness, projected height in the z-direction, and aspect ratio were chosen as

an input dataset to the clustering algorithm. As per the VGStudio Max reference

manual, the feature ‘diameter’ represents the diameter of the circumscribed sphere

of the defect [38]. The feature ‘sphericity’ indicates the ratio between the surface of

a sphere, with the same volume as the defect and the surface of the defect, as

expressed by Equation 2, whereas the ‘compactness’ can be expressed by the ratio

between the volume of the defect and the volume of the circumscribed sphere, as

shown in Equation 3 [38]. The aspect ratio is defined as the projected pore size in

the x-axis, divided by the projected pore size in the y-axis. The projected size in the

z direction, is the pore height perpendicular to the build plate. Voxel volume is

defined as ‘a value on a regular grid in 3-dimensional space’ analogous to pixels in

a 2D image.

  

 Equ. 2

  

 Equ. 3

Unsupervised clustering was applied to porosity features, which were obtained

from the XCT models for the 17 cylindrical parts selected across each of the 77

cylinders printed at the three gas flow rates investigated. The unsupervised

clustering model was implemented using Python Jupyter Notebooks, and the open-

source ML repository SciKitLearn [39]. The 7 input features used were: diameter;

voxel; surface area; compactness; sphericity; projected size in the z direction; and

aspect ratio.

3.5 OPTICAL MICROSCOPY EXAMINATION

The porosity of the printed components was also evaluated based on optical

microscopy examination of the sectioned components. This involved obtaining cross

sectional microscopy images at specific layers of the sectioned cylindrical parts, then

sectioning 8 randomly chosen cylindrical parts, obtained for parts selected from each

of the three gas flow levels investigated, using a Buehler IsometTM High Speed Pro

precision saw. The samples were ground using 2400 grit silicon carbide paper and

then polished using a 9 µm diamond paste. The exposed cross sections were then

etched by treating with hydrogen peroxide and silica solution. Optical microscopy

images were then taken using the Olympus DSX1000 Digital Microscope and the

results obtained at magnification of 624 and 275 times.

Numerical analysis of the microscopy images was facilitated based on their analysis

using ImageJ software. This Java-based image processing program uses greyscale

thresholds of the microscope images, as an input to the program, thus allowing the

determination of regions of porosity [40]. An example of ImageJ porosity analysis

applied to a micrograph sample is shown in Figure 22. The features that ImageJ

extracted about identified porosity were the ‘area’, ‘circularity’, ‘aspect ratio’,

‘roundness’ and ‘solidity’ of the 2D pore. Solidity refers to the ratio of a pore’s area to

its convex area [40]. The convex area is the smallest convex area that contains all

points within the pore. The aspect ratio in this case refer to the ratio of the largest axis

in a pore to the smallest axis in a pore. The circularity of a pore is defined in equation

4. Roundness is defined as given in equation 5, where ‘major axis’ represents the

largest axis within the pore [40].

  

󰇛󰇜 Equ. 4

  

󰇛󰇛󰇜󰇜 Equ. 5

Figure 22 An example of ImageJ porosity thresholding applied to a micrograph

image (Left) of a Ti-6Al-4V produced on the Renishaw RenAM 500M. Based upon

grayscale values of each pixel, each pixel in the micrograph is labelled as ‘Porous’ or

‘Non-Porous’ (Right), and geometric features relating to each individual pore are

calculated using the porosity analysis module available in ImageJ. The thresholded

image contains porous point (In Black) and solid material (In White). Note that while

the Bakelite mount surrounding the solid material is also black, this area was not

included in porosity analysis.

CHAPTER 4: RESULTS OF THE POROSITY ANALYSIS

CHAPTER 4: POROSITY ANALYSIS RESULTS

4.1 INTRODUCTION

This chapter provides the results of the porosity study carried out using XCT analysis

of the printed Ti-6Al-4V alloy parts, printed at the three Ar gas flow rates investigated.

It also details the results obtained from a cross-sectional analysis study of the alloy

parts, which was combined with ImageJ porosity analysis. Pore type results obtained

from both methods are discussed, as well as an analysis of the overall porosity

obtained using both methods. While a direct comparison of both methods cannot be

made due to the differing resolutions, as well as the fact that the CT scan provides

information on the entire cylinder, while the cross-section analysis provides details on

individual cross-sectional layers. Nevertheless, the outputs from both analysis

methods can be obtained.

4.2 COMPARISON OF POROSITY OBTAINED THROUGH XCT AND MICROSCOPY

This study compared the porosity results obtained using XCT and optical microscopy,

with the latter provide image data at two different magnifications (624 and 275 times).

The latter data was in-turn analysed using ImageJ, in order to evaluate the level of

porosity. The increased magnification dataset was used in order to obtain a better

resolution of the porosity observed. The lower magnification of 275X was used in a

comparison with the porosity data obtained from XCT. The XCT data was examined

using a Porosity Inclusion Analysis (PIA) module ‘Easy Pore’ available in VGStudios

XCT analysis software, as discussed in section 3.4. A reconstruction in VGStudios of

a cylinder produced at the same build plate location, in each of the three gas flow

builds is presented in Figure 23. The blue markings representing the porosity. Through

visual inspection of Figure 23, the marked increase in porosity with reducing Ar gas

flow rate is evident.

Figure 23 VGStudios XCT Reconstruction of gas flow cylinder sample produced at

same build plate location from high gas flow (36 per hour) (left); medium gas flow

(31 per hour) (centre); and low gas flow (26 per hour) (right)

Figure 24 Distribution of XCT Porosity across the build plates, based on

measurements obtained from 17 samples examined for each of the three gas flow rate

builds obtained from 17 samples examined for each of the three gas flow rate builds

Figure 24 shows a contour plot which was obtained based on an analysis of XCT

scans of each of the gas flow rate builds. The contour plot shows the average detected

porosity of each cylinder plotted at its location on the build plate. Again, it is evident

from this figure, that the low gas flow build contained a substantially larger amount of

porosity compared to the medium and high gas flow builds, with the medium gas flow

containing marginally more porous compared with the high gas flow build. From Figure

24 it is also clear that higher levels of porosity are obtained to the right of the contour

plot image, obtained for the low gas flow rate print. This indicates that the higher

porosity is in fact close to the gas inlet rather than away from it. This result is surprising

as it is anticipated that with the deposition of process by-products such as condensate

that higher levels of deposition would be obtained in the print bed region away from

the Ar gas inlet. Note the relatively homogeneous distribution of porosity for the print

beds obtained at medium and the high gas flow rates.

Figure 25 shows an example of a cross section image from the low gas flow taken at

275X magnification. This sample was from rod 77, which was printed close to the gas

inlet, and was found to contained considerable levels of porosity. This was also evident

based on the XCT analysis data (Figure 23).

Figure 25: An example Cross Section Image taken from the Low Gas Flow build,

demonstrating a considerable level of lack of fusion porosity

Figure 26: Comparison between images of Ti-6Al-4V obtained using XCT (a), and from

the approximately the same area obtained after cross sectioning, followed by

microscopy examination (magnification 275X) (b), for a sample printed at the low gas

flow rate. Note the large ‘key-shape’ LOF pore, with an approximate length of 800 μm

in the y-direction at point 1 on the XCT cross section (a), with the corresponding pore

in the microscope image (b).

In order to make a comparison between the porosity analysis methodologies, an

investigation into the minimum detectable diameter of pore associated with each

method was undertaken. The minimum diameter of pores detected using the XCT PIA

was approx. 80 µm, which is associated with selecting a minimum pore detection

volume of 60 voxels during the VGStudio Max PIA analysis step. This minimum

volume was selected to ensure that noise in the XCT scans was not falsely labelled

as porosity. This is thus a limitation in the pore resolution which can be obtained using

the PIA analysis approach. In order to help establish the accuracy of the XCT results,

optical microscopy examination of porosity in alloy cross sections were also examined.

Figure 26 provides an example of a comparison between XCT and cross section

optical micrograph of approximately the same layer region in the titanium alloy. It is

clear from this Figure that at approximately the same magnification level, that

microscopy facilitates the identification of smaller pores i.e., at points 3 and 4. A feature

of note in this image which was obtained for a part printed at low Ar flow rate, is that

the porosity is mainly associated with LOF porosity.

The minimum recorded pore diameter from ImageJ analysis of the Micrograph cross

section samples at an increased magnification of 624X was found to be 0.5 µm. In

comparison the minimum detectable diameter at a magnification of 275X was found

to be 1.3 µm.

Table 4 compares the average level of porosity recorded for the print builds obtained

at the three gas flow rates, when analyzed based on ImageJ examination of the

micrographs, along with the XCT measurements. The Micrograph images were taken

at two magnifications, as shown. There was a total of 55 images taken at 275X

magnification. While there was a total of 9 images taken at 624X magnification. In

each of the magnifications, as well as in the XCT analysis a reduction in overall

porosity is seen with increasing Ar gas flow rate. This is most likely since a reduction

in purging gas flow rate results in less removal of process by-products, which

increases the likelihood of defects, during the LPBF process [61].

Ar Gas Flow Rate:

XCT Porosity

Volume Percent

ImageJ

Micrograph

Porosity

(M=275X)

ImageJ

Micrograph

Porosity

(M=624X)

Low

0.21%

0.65%

3.64%

Medium

0.03%

0.10%

0.81%

High

0.01%

0.02%

0.4%

Table 4: Comparison between the porosity measurements obtained based XCT and

Micrograph ImageJ Porosity Measurements.

Although a direct comparison between XCT and micrograph results is not possible, it

is interested to note that the same trend is present in both methods. The highest level

of overall porosity in each method is present within the low gas flow rate builds, while

a decrease is observed in the medium gas flow rate build, and consequently the high

gas flow rate build.

4.3 CONCLUSIONS

This study investigated the effect of argon gas flow rate during the L-PBF printing of

Ti-6Al-4V on the resulting alloy porosity. XCT analysis demonstrated that the build

manufactured under a low gas flow rate (26 m3 per hour), had significantly increased

levels of porosity relative to the build manufactured with the medium (31 m3 per hour)

and high gas flow (36 m3 per hour) rates. This is most likely due to insufficient

removal of process by-products from the build plate because of a reduced gas flow

rate. The build manufactured with a high gas flow rate had broadly similar levels of

porosity to that manufactured with a medium gas flow rate. For a commercial

manufacturing process where Ar gas costs are a significant consideration, this would

indicate that the medium gas flow rate could be selected for routine production, in

order to reduce the level of Ar used during part printing. This is the case for the

RenAM 500M, where Renishaw’s recommended flow rate is the 31per hour,

‘medium’ rate.

The level of porosity obtained using XCT was compared with that obtained based

on cross sectional microscopy images of the printed alloy. Taking the example of

the low gas flow rate the porosity determined by XCT was 0.21%, while that obtained

using the micrograph examination at approximately the same magnification was

0.65%. The limited minimum detectable diameter which can be obtained using the

XCT analysis technique of 12.5 µm, is a significant factor to the porosity differences

obtained using the two techniques.

It is important to gain stress however, that due to the differing resolutions of these

two methods, they cannot be compared directly. Although micrograph data enables

the analysis of porosity at a smaller resolution than XCT, the sectioning of samples

required to obtain the micrograph is a time consuming process, and only reveals a

fraction of the total porosity present within a sample. XCT analysis is faster, and

produces porosity information on entire samples, however at a lower resolution.

CHAPTER 5: UNSUPERVISED CLUSTERING AND CLUSTER NUMBER

EVALUATION:

CHAPTER 5: UNSUPERVISED CLUSTERING AND CLUSTER NUMBER EVALUATION

5.1: INTRODUCTION

In Chapter 4 the overall level of porosity was evaluated based on both XCT and optical

microscopy examination of the Ti-6Al-4V alloy parts. As detailed in the literature review

for these LPBF alloy parts there are generally three different forms of microstructural

porosity considered: Gas pores; Keyhole pores; and Lack of Fusion pores. In addition

to their variation in morphology, the type of porosity also impacts on the mechanical

properties of the resultant component [117][118]. Lack of Fusion pores have the

largest impact on mechanical components due to their ability to act as stress

concentrators, and subsequently crack initiators [119][120]. Keyhole pores also have

a considerable impact upon mechanical performance, although not as drastic as Lack

of Fusion pores [117]. Therefore, it is important to be able to distinguish between the

three forms of microstructural porosity.

This chapter provides the results for the application of the Gaussian Mixture Model’

(GMM), unsupervised machine learning technique as an approach to evaluate the type

of porosity present in the parts. This examination is based on the XCT and microscopy

datasets for porosity analysis of the Ti-6Al-4V cylinders. In order to carry out this

investigation it is necessary to determine the number of clusters present within the

data based on an investigation of clustering models. This is followed by the

implementation of four different statistical approaches to determine the number of

clusters present within the XCT and micrograph datasets. The four approaches

investigated were a dendrogram approach, an elbow plot approach, a Bayesian

Information Criterion (BIC) score approach, as well as a Silhouette Score approach.

Finally, the conclusions from the implementation of the GMM approach to the three

datasets will be reviewed. The unsupervised clustering results from the GMM model

at each gas flow rate will be presented in each of the XCT and micrograph datasets.

5.2: UNSUPERVISED CLUSTERING

Unsupervised clustering was applied to three datasets obtained from the XCT and

optical microscopy analysis (evaluated at two magnifications). The XCT dataset

contained 95,489 datapoints obtained from the total of 51 cylinders examined at the

three gas flow rates investigated. Each datapoint containing 7 independent features,

as well as a categorical variable ‘Gas Flow’. The ImageJ analysis of optical microscopy

image datasets, both contained 5 features, and the same Gas Flow variable. The log

magnification dataset was taken at a magnification of 275X, containing 134,987

datapoints, while that obtained at the higher magnification of 624X, containing 249,826

datapoints.

The GMM model is a probabilistic model, that assumes all data points were generated

from a finite number of Gaussian distributions with unknown parameters [121]. For this

study the GMM model was implemented using Python Jupyter notebooks. GMM

models can be thought of as a generalised K-Means clustering model that incorporates

the covariance structure of the data. GMM clustering is also soft clustering in

comparison to K-Means, which is hard clustering. A cluster with regards to data

science can be defined as grouping datapoints together into groups (or clusters) such

that points in each cluster are more like other points within that cluster than points

within other clusters [122]. This is the basis of unsupervised clustering, which is used

in order to examine clusters present within datasets.

The covariance of the model refers to the covariance matrix of an n-dimensional

Gaussian distribution [121]. The covariance constraint for GMM models can be one of

four types: Spherical; Diagonal; Tied; Full. In higher dimensions, the univariate and

bivariate Gaussian distribution can be rewritten using a mean vector µ, and an n-by-n

covariance matrix Σ. In 2 dimensions, the Gaussians parameters may look like this

[121]:

󰇣󰇡

󰇢󰇡









󰇢󰇤 Equ. 6 [121]

The right-side matrix in this equation defines the covariance matrix. The values within

this matrix decide what covariance type fits the data [123]. In spherical covariance, off

diagonal elements are all 0, with all diagonal elements being of equal value. All

nondiagonal elements being 0 indicates parameters have no correlation, while

equivalent diagonal values result in a circular probability distribution indicating the

spread of the Gaussian distribution along these axes is the same. Diagonal and tied

covariance imply 0 nondiagonal values, while diagonal values can be any nonzero

values. The difference between tied and diagonal, is that in diagonal clustering

Gaussian distributions for each cluster can have differently oriented probability

distributions whereas in tied all Gaussian distributions must be the same orientation.

Full covariance allows for correlation between variables, meaning nonzero values for

off diagonal covariance matrix entries.

Figure 27 shows the results obtained when all covariance constraints were plotted, for

an example open source Scikit learn dataset known as ‘Iris’[121]. The data generated

is four dimensional, however only two dimensions are plotted, thus some points are

separated in other dimensions. Each datapoint belongs to one of three classes,

namely Setosa, Versicolor, and Virginia. As can be seen in the spherical covariance

sub-plot in Figure 27, resultant clusters are spherical in shape, although circular in the

image due to being reduced to 2 dimensions. Diagonal covariance results in clusters

that may be independently oriented either elliptically or spherically, however this must

be along the coordinate axes, as seen in Figure 27. Tied covariance differs from

diagonal covariance, in that clusters may be oriented in any direction regardless of

coordinate axes, however all clusters must be oriented identically. Full covariance then

allows for clusters to independently adopt any shape.

Figure 27: Covariance Constraint parameters for GMM plotted on open source ‘Iris’

data. Training datapoints marked with crosses, while test datapoints marked with dots.

The GMM model was trained using the training dataset, while evaluated then upon the

test set [121].

The GMM model required the input of two parameters: the number of clusters, along

with the covariance constraint [121]. For this research, full covariance was

implemented in order to allow for any possible cluster orientation.

5.3: CLUSTER NUMBER EVALUATION

In most clustering problems, the model requires the user to input the number of

clusters present within the dataset, the clustering models will then attempt to split the

data into the predetermined number of clusters [20]. There are a variety of approaches

that can be taken in order to determine the number of clusters present, which can then

be used as an input to the clustering algorithm. In this thesis four approaches were

investigated as follows –hierarchical clustering evaluation, elbow plot evaluation,

Bayesian Information Criterion, and silhouette score evaluation. All four approaches

are discussed in-turn, there were all implemented in Python Jupyter Notebooks, using

Scikitlearn open-source packages.

5.3.1: HIERARCHICAL CLUSTERING AND DENDROGRAM APPROACH

This is a distance-based approach, based on inputs of the Euclidean distance,

Manhattan distance, or Mahalanobis distance, to calculate the closeness of the data

points [20]. A limitation of this type of clustering, however, is that it cannot handle

extensive datasets and takes a higher amount of computing power and time [42]. One

of the advantages of hierarchical clustering is that the results are represented

graphically through a ‘dendrogram’, which shows the clustering approach at different

hierarchical levels [42]. The dendrogram also informs the number of cluster choices

that will best depict the data groups. To find the optimum cluster choice, the maximum

vertical distance of the dendrogram is transversed by a horizontal line, this is marked

as the red line in Figure 28, using an example dendrogram. The number of vertical

lines in the dendrogram intersected by the horizontal line, that can spread the entire

distance vertically without intersecting a cluster, is the optimal value for the number of

clusters. Hierarchical clustering was carried out for both the XCT and micrograph

datasets, in order to determine the optimal number of clusters. However, the

dendrogram approach may not always yield an optimal cluster number, as evident in

Figure 28, where the largest vertical distance (above clusters A and B, marked in

green) can mean any of 2, 3 or 4 clusters. In this case, other methods of determining

cluster number, such as those discussed in sections 5.3.2 to 5.3.4 of this thesis can

be used.

Figure 28: Two-dimensional feature space, with 6 points and resultant dendrogram.

As can be seen from the dendrogram, no clear cluster number is evident. The largest

vertical line (green) can be seen to intersect any of 4, 3 or 2 vertical lines depending

on where the horizontal (red) line is placed [123]

5.3.2: HIERARCHICAL CLUSTERING RESULTS

Figure 29: Hierarchical Clustering Dendrogram plots for (a) Low Gas Flow Rate (26

per hour) (b) Medium Gas Flow Rate (31 per hour) (c) High Gas Flow Rate (36

per hour)

Figure 29 shows the hierarchical clustering dendrograms for the three gas flow rates

investigated. In each of the images, the blue section of the dendrograms contains the

largest vertical distance. In (a) the ideal cluster number is 2. A horizontal line

intersecting the left side blue vertical line here would intersect one other vertical line

for most of this line, indicating that the ideal cluster number in this gas flow is 2.

However, in the medium gas flow, the ideal cluster number is unclear. In (b), the left-

hand blue line is the largest vertical line again, however a horizontal line intersecting

this line could possibly intersect any of 2, 3, 4 or 5 clusters, as no clear cluster number

stands out in this graph, introducing an element of subjectivity into the choice of the

optimum cluster number. However, in (c) the optimum cluster number similarly to (a).

appears to be 2. The lack of a clear cluster number from this dendrogram approach

indicated that this method is not a suitable method for determining cluster number.

The subjectivity in determining the cluster number in (b) led to further investigations

into cluster number determinations. Another aspect that required alternative methods

of cluster determination, was that soft clustering methods such as GMM that use a

probabilistic Gaussian distribution to determine the most likely cluster for a datapoint,

don’t use hierarchical clustering to determine cluster number. This method is more

suited to hard clustering methods, such as K means clustering [123].

5.3.3: ELBOW PLOT APPROACH

This approach is widely used in cluster analysis, as it generally produces an easy to

interpret result [48]. In this approach, the average distance between a datapoint, and

its cluster centre is plotted, at every cluster number value. The user then looks for an

‘elbow’ or a drastic change of slope from steep to shallow, in order to determine the

optimum number of clusters (see Figure 30 (left)). This elbow point indicates the

optimum number of clusters, as although the average distance to cluster centre may

decrease with an increased cluster number at this point, the drastic change in slope

indicates that this change per additional cluster is only marginal. This is a case of

diminishing returns, where additional clusters increase complexity without reducing

the average squared distance sufficiently. The main drawback with this method, similar

to the dendrogram approach, is its subjectivity, as the elbow point may not always be

definite, and this introduces an element of choice in the cluster value. Figure 30 shows

two cases, one (left) where the elbow is clear, and another (right) where no definite

elbow is present [48]. In this graph the sum of squared errors is plotted against cluster

number in comparison to average squared difference.

Figure 30: Elbow plot comparison, with definite elbow point present (left), and no elbow

point present (right). This lack of clear elbow in plot indicates that a new cluster number

evaluation method required [48]

5.3.4: ELBOW PLOT RESULTS

Figure 31: Elbow Plots for XCT analysis of LPBF produced Ti-6Al-4V cylinders

produced at: (a) Low Gas Flow Rate (26 per hour) (b) Medium Gas Flow Rate

(31 per hour) (c) High Gas Flow Rate (36 per hour)

Figure 31 shows the elbow plots for the three gas flow rates investigated in this thesis.

It is evident from the three plots that no clear elbow occurs in any of the three plots.

When data from all three gas flows were collated into one combined dataset, the elbow

plot did not indicate a clear cluster number either. Because of this ambiguity, the Elbow

plot was not found to be suitable for the evaluation of cluster number for this

investigation.

5.3.5: BAYESIAN INFORMATION CRITERION APPROACH

The Bayesian Information Criterion (BIC) is a method for scoring and selecting a

model, or for determining the optimum number of clusters for a defined model [96].

The BIC score is named for the field from which the value was derived: Bayesian

probability and inference This score is used for models that fit under the maximum

likelihood framework. BIC is calculated for a model using equation 7 [96]:

 󰇛󰇜 󰇛󰇜 Equ. 7

Where d is the number of parameters in the model and N is the number of examples.

The BIC score is minimised, with a lower score indicating a better model. BIC attempts

to reduce the effect of overfitting through the introduction of the penalty term 󰇛󰇜,

which penalises models with large number of parameters [98]. Consequently, the BIC

score approach, prefers simpler models.

As a result of the derivation of the BIC score from the Bayesian probability framework,

if a series of models under evaluation contains a ‘true model’, the probability that BIC

will indicate the true model increases with an increasing number of samples N [96]. A

disadvantage of the BIC score is that for small datasets it tends to favour oversimplistic

models [96].

5.3.6: BIC SCORE RESULTS

Figure 32: Low Gas Flow XCT data BIC values vs Cluster number for GMM clustering

Figure 32 shows a BIC plot for the low gas flow data obtained from the XCT analysis

of the Ti-6Al-4V cylinders. This plot shows the BIC score obtained from a GMM applied

at each cluster value from 1 to 14 clusters. This resulted in 4 individual line graphs, for

each of the GMM covariance types, as discussed in section 5.2. No minimum BIC is

reached in any of the covariance types, with each type converging to some minimal

value far outside the above cluster interval. This suggests that the GMM is having

difficulty deciding between cluster memberships. This implies that BIC scores in this

case cannot provide a clear indication of the correct number of clusters, as no definitive

minimum exists.

It is interesting to note that the Full covariance yielded the smallest BIC value in this

specific case, followed by diagonal and tied, with spherical covariance yielding the

largest BIC value. This indicates that there is some probable relationship between

variables in the XCT analysis data. The fact that spherical covariance is approximately

an order of magnitude larger than the other three covariances, implies that spherical

GMM clusters are most probably not the most accurate clustering technique.

As there were three gas flow rates in the LPBF process investigated in this study, as

well as porosity data from three different sources, in order to combine the BIC score

analysis of each of these methods a three-by-three matrix plot is presented in the

appendix section. In each case, the optimal number of clusters was still unclear.

5.3.7: SILHOUETTE SCORE APPROACH

Silhouette scores is a clustering evaluation metric used to calculate how well a

clustering technique grouped datapoints [99]. Its values range from [-1,1]. A value of

1 indicates that clusters are well apart from each other, and clearly distinguished. A

value of 0 means that clusters are indifferent to each other, while a score of -1 indicates

clusters are incorrectly assigned.

The silhouette score for a datapoint ‘i’ is calculated from the following equation:

 

󰇛󰇜 Equ. 8 [99]

Where  is the inter cluster distance, and  is the intra cluster distance. The inter

cluster difference is the average distance to the closest cluster to datapoint ‘i’, that it

is not part of. Mathematically this is given in Equation.







󰇛󰇜

 Equ. 9 [99]

Where  is the closest cluster to ‘i’. The intra cluster distance is defined as the

average distance between datapoint i and other datapoints within the cluster it is a part

of. Mathematically this is given in Equation X.

 

 󰇛󰇜

  Equ. 10

The overall silhouette score for a dataset can be calculated as the average silhouette

score for all datapoints within the dataset. Graphically, the intra and inter cluster values

are shown in Figure 33.

Figure 33: Depiction of values used in silhouette score calculation [99].

5.3.8: SILHOUETTE SCORE RESULTS

The fourth and final cluster number determination method implemented was the use

of silhouette scores. As described in section 5.3.4 silhouette scores range from -1 to

1, with a value of 1 indicating a perfect cluster number. In this calculation, GMM models

with full covariance were fitted with cluster values ranging from 2 to 9 and average

silhouette scores at each cluster number were obtained. This resulted in 9 plots owing

to the three gas flows and three data sources. Figure 34 shows 3 plots for each of the

data sources, with 3 gas flows plotted per data source in each graph.

Figure 34: Silhouette scores for GMM plot with full covariance per cluster number for

each data source. Each Data source containing three gas flow rates. Note that in (c)

although the silhouette scores for a cluster number of 2 and 3 appear identical in the

High and Medium gas flow, the value at a cluster number of 2 is marginally larger.

Figure 34 shows the silhouette score for a GMM plot with full covariance at each

cluster number. A cluster number of 2 achieves the highest silhouette score for each

of the gas three gas flow rates investigated. This was the first definitive indication for

a cluster number based on the four approaches investigated in this study. Note that in

the case of the optical microscope datasets that for the medium and high gas flow

datasets, although the cluster numbers of 2 and 3 appear to have an identical

silhouette score, a cluster number of 2 has a marginally larger silhouette score than 3

in both cases. Therefore, for GMM analysis of the datasets, a cluster number of 2 was

used. It was interesting to note that for the 9 individual line plots, the same optimal

cluster number was obtained.

5.4: CLUSTER NUMBER RESULTS SUMMARY

In this study the performance of four different approaches were investigated in order

to determine cluster number in each dataset. Initially, hierarchical clustering was

implemented, however no clear cluster number was evident from the produced

dendrogram for any of the data sources. Following on from this, an elbow plot for each

of the data sources was produced. Similarly, to the hierarchical clustering issue, no

clear cluster number was evident. Subsequently BIC scores were calculated at each

cluster number for each gas flow in each of the micrograph sources and the XCT. A

lower BIC score indicates the most accurate cluster number value, however in each

data source BIC scores never converged to an accurate cluster number value perhaps

indicating that the GMM struggled to accurately assign cluster membership to certain

datapoints. The fourth method evaluated involved calculating silhouette scores for

each of the data sources. It was concluded from the fourth study that a cluster number

of 2 was the most appropriated for use with each data source.

5.5: UNSUPERVISED CLUSTERING USING GMM RESULTS

The results of GMM clustering with full covariance applied to the XCT and both

micrograph datasets are presented in the following section. Initially the XCT results

are presented, followed by the micrograph results obtained at a magnification of 275X,

and finally the micrograph results obtained at 624X. Porosity sphericity data is

presented with the XCT data, while circularity is presented in conjunction with the

porosity obtained using optical microscopy examination. The data is provided based

on the 2 clusters present within each of the data sources, as determined in the

previous sections.

5.5.1: GMM PLOT FOR XCT DATA

Figure 35: GMM Results for XCT Analysis data from (a) Low (b) Medium (c) High

Gas Flows. Total of 95489 Pores

In Figures 35(a), (b), and (c). the GMM results obtained from an analysis of the XCT

data are presented. The cluster membership average feature values of both clusters

at each gas flow are presented in table 5

For each of the three gas flow rates investigated, clusters were initially labelled 0 and

1. Through examination of the average features for each cluster, presented in table 5

it was decided that cluster 0 in each gas flow would be labelled as ‘Regular’ type

porosity, with cluster 1 being labelled ‘Irregular porosity’. The Irregular cluster

encompasses a substantial amount of both Keyhole and Lack of Fusion porosity. The

Regular pores have diameters of less than approx. 0.3 mm, and these have a large

contribution from gas type porosity. This labelling of clusters into Regular or Irregular

type porosity, enabled a comparison of pore type morphology across gas flow rates.

Gas

Flow

Diameter

[mm]

Voxel

Surface

[]

Sphericity

Compactness

Projected

Size z

[mm]

Aspect

Ratio

Low

0.18

155

0.04

0.52

0.11

1.07

Low

0.45

137

0.34

0.31

0.06

0.27

1.08

Medium

0.18

149

0.04

0.53

0.11

1.06

Medium

0.39

980

0.24

0.33

0.07

0.22

1.08

High

0.17

139

0.04

0.56

0.13

0.10

1.05

High

0.38

960

0.23

0.34

0.07

0.19

1.05

Table 5: Cluster Average Feature Values across each Gas Flow for XCT data. Dark

rows represent Irregular clusters, and light rows represent Regular clusters

Gas Flow Rate

Regular Porosity

Proportion

Irregular Porosity

Proportion

Low (26 per hour)

79.6%

20.4%

Medium (31 per hour)

85.7%

14.3%

High (36 per hour)

90.6%

9.4%

Table 6: Pore Type proportion at each gas flow obtained from XCT data

The proportion of each pore morphology type (Regular or Irregular), is presented in

Table 6. This demonstrates that as the proportion of Regular type porosity increases

with increasing gas flow rate, there is a decrease in the level of Irregular pore type.

This would indicate that an increase in gas porosity associated with an increased

purging gas flow rate in the LPBF process, may be due to increased gas entrapment

in the molten powder bed during the solidification process. This in combination with

the increased removal of process by-products, which would be associated with the

generation of lack of fusion porosity, therefore results in the decreased Irregular

proportion at higher gas flow rates.

It can also be seen through comparing plots 34(a), (b) and (c), that the Irregular pores

in the low gas flow build, are much larger than in the medium and high gas flow builds,

as well as have a more non spherical morphology. A possible explanation is that this

is associated with a considerable increase in lack of fusion porosity in the low gas flow

build, as this form of porosity tends to be the largest and most irregular. The average

Irregular pore diameter and surface area in the low gas flow is 0.449 mm and

0.338respectively, in comparison to that obtained at the high gas flow rate of

0.376 mm and 0.232 respectively.

5.5.2: GMM PLOT BASED ON MICROSCOPY DATA

5.5.2.1: OPTICAL MICROSCOPY IMAGES (275X)

Figure 36: GMM Results for Optical Microscopy Analysis data from (a) Low (b) Medium

Figure 36 shows the GMM clustering results for the Optical Microscopy ImageJ

porosity analysis data, obtained at lower magnification (275X). Similarly, to section

5.5.1, two clusters were used as an input to the GMM model, as determined using the

silhouette score analysis. The average feature values for both clusters at each gas

flow are presented in table 7. At each gas flow rate, one cluster (the group labelled as

0 by the GMM model) contained pores that were far smaller and much more irregular

than the other cluster (the cluster labelled as 1 by the GMM model). Hence, it was

decided that cluster 0 would be referred to as the ‘Regular’ cluster group, and the other

group be referred to as the ‘Irregular’ cluster group.

Gas

Flow

Cluste

Area

[]

Circularit

Aspect

Ratio

Roundne

Solidit

Label

Low

0.90

1.64

0.68

0.89

Regular

Low

2190

0.48

2.55

0.49

0.75

Irregular

Medium

0.93

1.77

0.70

0.92

Regular

Medium

487

0.43

2.06

0.54

0.66

Irregular

High

0.87

2.30

0.65

0.89

Regular

High

1103

0.51

1.91

0.60

0.89

Irregular

Table 7: Cluster Average Feature Values across each Gas Flow obtained from

microscopy images (Magnification = 275X)

Based upon the class labels decided upon through the values in table 7, the pore type

proportions of both Regular and Irregular clusters in each gas flow are presented in

table 8.

Gas Flow Rate

Regular Porosity

Proportion

Irregular Porosity

Proportion

Low (26 per hour)

74.3%

25.7%

Medium (31 per hour)

95.4%

4.6%

High (36 per hour)

93.4%

6.6%

Table 8: Pore Type proportion at each gas flow based on Optical Microscopy data

(M=275X). Total of 55 Samples

Like table 6, the low gas flow exhibits by far the lowest proportion of Regular porosity.

However, in contrast to table 6 the medium gas flow exhibits the largest proportion of

Regular porosity rather than the high gas flow, with a difference of 2% between

Regular pore type proportion. This is differing behaviour than that observed in the

GMM clustering of the XCT behaviour. It is interesting to note however that although

the Regular pore proportion in the low gas flow is comparable to the XCT low gas flow,

the Regular pore proportion in the Optical Microscopy medium and high builds was

10% and 3% higher than that obtained for samples analysed using XCT at the

corresponding gas flows.

5.5.2.2: OPTICAL MICROSCOPY MAGNIFICATION 624X

Figure 37: GMM Results for Optical Microscopy Analysis data from (a) Low (b) Medium

Figure 37 shows the GMM plots for the increased magnification Optical Microscopy

data at each of the gas flow rates. Important to note in these graphs is the x axis, which

is an order of magnitude larger in the low gas flow compared to the high gas flow. The

only gas flow in this case to exhibit considerable amounts of Irregular porosity was the

low gas flow, with the medium and high gas flows only detecting 3 and 1 Irregular

pores respectively.

A consequence of the medium and high Irregular cluster being so small and skewed

towards large porosity is that the average area of these pores was considerably larger

than the Irregular cluster in the low gas flow rate. In both previous clustering

applications, the Irregular class in the low gas flow contained the largest porosity (by

average area) and this should be the case in this situation also due to the large amount

of extremely large-scale porosity in the low gas flow.

At each gas flow, two clusters were present. At each gas flow, the cluster group ‘0’

contained that were far smaller and much more regular in shape than the other cluster.

Consequently this cluster was referred to as the ‘Regular’ cluster in each gas flow,

while the other cluster was referred to as the ‘Irregular’ cluster.

The average feature values for the clusters in Figure 37 are given in table 9. The

average area of Irregular pores in the low gas flow is considerably reduced due to the

large amount of small-scale porosity relative to the other 2 gas flows, as evident in

Figure 37.

Gas

Flow

Cluster

Area

[]

Circularity

Aspect

Ratio

Roundness

Solidity

Label

Low

1.3

0.954

1.585

0.718

0.938

Regular

Low

275.0

0.454

5.549

0.312

0.737

Irregular

Mediu

2.7

0.914

1.793

0.675

0.904

Regular

Mediu

18154.7

0.178

2.237

0.531

0.612

Irregular

High

2.1

0.906

1.960

0.706

0.908

Regular

High

7841.9

0.348

1.215

0.823

0.874

Irregular

Table 9: Cluster Average Feature Values across each Gas Flow for Optical

Microscopy (Magnification = 624X)

In table 8, at each gas flow the cluster labelled by the GMM model as cluster 0

contained small and regular pores, evident through their reduced average area and

increased average circularity. It was consequently decided that these clusters would

be referred to as the ‘Regular’ cluster, and cluster 1 would be referred to as the

‘Irregular’ cluster.

Based upon the class labels decided upon through the values in table 9, the pore type

proportions at each gas flow are present in table 10. There is again an increase in the

proportion of Regular pores across all builds, with both the medium and high builds

containing 99%+ Regular type porosity, and the low gas flow Regular pore proportion

increasing by 14%.

Gas Flow Rate

Regular Porosity

Proportion

Irregular Porosity

Proportion

Low (26 per hour)

89.080%

10.920%

Medium (31 per hour)

99.997%

0.003%

High (36 per hour)

99.998%

0.002%

Table 10: Pore Type proportion at each gas flow in micrograph data (M=624X). Total

of 9 Samples

5.6: DISCUSSIONS AND CONCLUSIONS

The focus of this study was the evaluation of unsupervised machine learning to help

cluster the type of porosity present in the Ti-6Al-4V alloy parts. The GMM analysis

was carried out on both the XCT data, as well as on ImageJ data obtained from

cross sectional microscopy images of the alloy parts both at a similar magnification

as used for the XCT examination, as well as at a higher magnification. Porosity

analysis through XCT is limited by the resolution of this analysis technique. A further

limitation is the additional reduction in resolution, which results from the application

of the VGStudio Max PIA module to the XCT data, this limited the lowest resolution

to approx. 80 µm. In contrast significantly higher levels of porosity was identified

based on the use of the microscopy analysis data.

The unsupervised GMM analysis of XCT data demonstrated that ‘Regular’ pores are

the most common pore type for all three gas flow rate builds. The parts printed at

the higher gas flow rate in addition to having the lowest porosity, also had the largest

proportion of Regular pores at 91%. In contrast, parts built under a low gas flow rate

had a high proportion of ‘Irregular’ porosity, with the proportion of Regular pores at

80%. The pore size and Irregular shapes as demonstrated based on the microscopy

examination, indicating that the Irregular pores at low gas flow were largely

associated with LOF porosity, while at high gas flow were largely associated with

Key-Hole porosity.

Using the method of silhouette scores to search for the optimal number of natural

clusters present in the dataset, it was concluded that the optimal number of clusters

was 2, for all three gas flow rate build. The reason for this optimal number of 2 rather

than 3 clusters for the three builds investigated, may be that significant levels of both

LOF and Key-Hole pores did not simultaneously occur in parts from the same gas

flow rate build.

In summary, XCT has many advantages as a method for porosity analysis over that

of micrograph analysis as it is non-destructive, less time consuming, and gives

information on the entire component rather than an individual cross section. The

VGStudio data can be successfully inputted into the GMM unsupervised machine

learning technique, to quantify the type of porosity present. A difficulty however is

the instrument resolution, which is further limited in order to avoid system data

‘noise’ when using the VGStudio Max PIA module. Based on a comparison between

the micrograph and XCT analysis using GMM, this unsupervised machine learning

approach has been successfully applied as a method for the clustering of the

porosity distribution within alloy parts with varying types of porosity.

CHAPTER 6: SUPERVISED CLASSIFICATION AND EVALUATION

6.1: INTRODUCTION

This chapter details the results of an investigation of the use of supervised

classification algorithms, as a machine learning approach to differentiate between

Gas, Keyhole and Lack of Fusion pores. The investigation was carried out using the

same ImageJ porosity analysis data obtained from the micrographs datasets, which

were used to evaluate the unsupervised machine learning approach detailed in

Chapter 5. The eight algorithms studied were: K-Nearest Neighbour (KNN); Decision

Tree Classifiers (DTC); Naïve Bayes (NB); Support Vector Machine (SVM); Logistic

Regression (LR); Multi-Layer Perceptron (MLP); Extreme Gradient Boosted

Classification (XGB) and Gradient Boosted Classification (GB). These algorithms were

selected due to their previous application in the field of Additive Manufacturing, as

detailed in Chapter 1 (Table 1). All algorithms are implemented using their default

Scikit Learn parameters, in this study.

This chapter will initially discuss the datasets used in this study, followed by how

supervised classification machine learning is implemented. Then the four metrics used

to evaluate the algorithms performance are discussed. The results of the classification

study will then be presented, followed by a discussion and conclusions.

6.2: SUPERVISED CLASSIFICATION

6.2.1: DATASET DESCRIPTION

In this study, two separate datasets were used, the first was obtained from the low

(275X) magnification ImageJ porosity analysis dataset obtained from the sectioned Ti-

6Al-4V samples. This was also used in the unsupervised clustering study described in

Chapter 4. In total 55 samples from this sample set were examined, based on cross

sections of the printed alloy samples. This dataset will be referred to as the ‘Gas Flow’

dataset throughout this chapter. The XCT dataset was not evaluated in this study, as

it was considerably more difficult to develop a training dataset from the 3D images. A

second dataset referred to as the ‘Test Set’ throughout this chapter, was obtained from

a separate Ti-6Al-4V alloy printing study, which was carried out using the Renishaw

RenAM 500M system, as detailed in Chapter 3. The same sectioning methodologies

were applied to the cylinders printed for this study, as for the Gas Flow dataset, with

cross sections obtained for microscopy analysis (in this case for 16 samples). As

before an ImageJ porosity analysis dataset was obtained.

Each of the ImageJ porosity datasets contained five features, namely: Area;

Circularity; Roundness; Solidity; and Aspect Ratio. A description of these features is

available in chapter 3 ‘Optical Microscopy Examination’, a manually labelled column

called ‘Pore Type’ is also included. The Gas Flow dataset contains 1082 pores, while

the smaller ‘Test Set’ dataset contains 482 pores. Example cross section images from

each sample set is shown in Figure 38.

Figure 38: Examples cross section images obtained from the two sample sets referred

to in this chapter with the Gas Flow sample shown on the left and that obtained from

the Test Set sample set, shown on the right

The manual labelling of the ‘Gas Flow’ alloy cross sections was performed through a

visual examination of the microscopy images. Lack of fusion and keyhole pores were

readily identified due to their large cross-sectional area, while the distinguishing

characteristic between these morphologies was the more irregular cross sections

evident in the lack of fusion class. Gas type porosity was identifiable as smaller pores,

which was generally found to occurred in clusters within the alloy, in contrast to the

other two pore types.

6.2.2: CLASSIFICATION IMPLEMENTATION

For model evaluation in supervised learning, the model must be evaluated on data

that it has not yet seen, to avoid what is referred to as ‘peeking’ [100]. This is to avoid

the model being exposed to the value or category it is about to predict, while it is being

fit, as this can lead to overfitting.

In supervised classification analysis, in order to evaluate model performance, two

different methods can be used. The first method is known as ‘K-Fold Cross Validation’.

This method involves splitting the data into ‘K’ distinct sections or folds and fitting the

chosen model on K-1 folds [100]. The model is then tested on the Kth fold, and the

amount of incorrectly classified samples is recorded. This is then repeated K times,

using each fold, as a test set once. Schematically this is show in Figure 39, for K=5.

The error is then averaged over the K folds. The test set can be seen moving through

the entire dataset from left to right in this Figure. The advantage of this method is that

instead of using 

 as a test set for algorithm performance, the entire dataset acts as a

test set.

The second method is simply training the models upon one dataset, and then

evaluating them upon a second separate dataset. Both methods are used in this

thesis. 5-Fold Cross Validation is performed upon the Gas Flow Set, and then the

models will be trained upon the Gas Flow dataset and evaluated on the Test set. This

will be implemented twice, once for Gas/Non-Gas pores, and secondly for

Keyhole/Lack of Fusion pores.

Figure 39: 5-Fold Cross Validation Example showing how the 20% of the total data

(indicated in grey) acting as a test set, moves through each portion of the dataset [100]

6.3: CLASSIFICATION EVALUATION

For supervised classification models, model evaluation is relatively straightforward

compared with other machine learning techniques such as unsupervised clustering

models, due to the input vectors in supervised classification models having a label.

This label is known as the ‘Ground Truth’ label, and allows for model predictions to

be classified as correct or incorrect.

In this study, rather than a multiclass classification, two binary classifications are

made. The two classifications used for this study are Gas/Non-Gas, and Keyhole/Lack

of Fusion. This implies that each of the Gas Flow and Test sets will be tested twice.

Firstly, with each pore being labelled as Gas/Non-Gas (Keyhole and Lack of Fusion),

and then secondly this Non-Gas subset shall be evaluated for Keyhole/Lack of Fusion

pores. This shall result in 4 sets of results, two 5-fold cross validation results on the

Gas Flow Set, and two further evaluations on the Test Set.

Predictions made by the a classification model in the case of binary classification can

be encapsulated in a ‘Confusion Matrix’. An example of a Confusion Matrix (CM) is

given in Figure 40, where TP, FP, FN and TN correspond to True Positive, False

Positive, False Negative, and True Negative respectively [101]. This CM can

encapsulate every single prediction made by the classifier, by labelling one class as

truth, and one class as false. For example, if Lack of Fusion pores are labelled as true,

and Keyhole pores are labelled as false, then every correct prediction made by the

classifier shall exist in the green TP or TN sections of Figure 37. However incorrect

predictions shall exist in the red sections at FP or FN.

Figure 40: Example Confusion Matrix for a binary classification problem [101]

Different measures can be obtained from the confusion matrix, such as accuracy, false

positive rate and false negative rate [101]. These measures can be used in order to

calculate classification metrics such as the Accuracy; the F1-Score; the Recall (for a

specified class); and the Area Under Curve (AUC) Score. The following section

provides some background as to how each of these measures are calculated.

6.3.1: GENERAL ACCURACY

General accuracy is defined as “the number of correct predictions divided by the total

number of predictions”. It provides a value indicative of model performance in

successfully classifying samples (in this cases pores). Mathematically this can be

written as shown in Equation 11 [101].

  

 Equ. 11

Where TP, TN, FP, and FN correspond to the confusion matrix labels in Figure 40.

6.3.2: AREA UNDER CURVE (AUC) SCORE AND RECEIVER OPERATOR

CHARACTERISTIC (ROC) CURVE

In supervised classification, each model has what is called a probability threshold

[101]. When training the algorithm is completed, and a new sample is classified, it is

assigned a probability of belonging to the ‘positive’ or ‘truth’ class. If this probability

exceeds the probability threshold, it is labelled as a ‘positive’ class.

The total number of true positives, false positives, false negatives, and true negatives

are recorded for a classification models performance upon a test set. These measures

are used in order to compute a True Positive Rate (TPR) and a False Positive Rate

(FPR).

TPR is defined as the number of true positives correctly identified as true, or

mathematically by equation 12 [101]:

  

 Equ. 12

FPR is defined as the number of negative predictions that are incorrectly identified as

true, or mathematically by equation 13 [101]:

  

 Equ. 13

To combine the two TPR and FPR measures into a single metric, the TPR and FPR

are plotted for a series of different probability thresholds within the model. The

resulting graph is then known as the ROC curve, and both FPR and TPR must be

within the range 0 to 1 (inclusive of both 0 and 1).

The Area underneath the ROC curve is known as the AUC score for that model [101].

An ideal classifier has a TPR of 1, and an FPR of 0, regardless of probability thresholds

within the model. This results in an ideal AUC score of 1. Hence, the higher the AUC

score, the better the performance of the model at distinguishing between the classes.

Some example ROC curves are plotted in Figure 41, in comparison to what is

considered as a ‘no skill’ classifier (similar to that of flipping a coin, where the

probability threshold is 0.5). Models whose ROC curve approaches a TPR of 1 and an

FPR of 0 are deemed better classifiers. A high AUC score indicates a ‘robust’ model,

in that a randomly chosen positive sample is most likely indeed positive, regardless of

the probability threshold within the model.

Figure 41: ROC Curves for 3 example models compared with flipping a coin. Better

models are shown approaching the behaviour of a perfect classifier [101]

Probability threshold refers to the decision threshold value for converting a class

probability into a class label in classification problems, i.e. the probability that a pore

belongs to either the Gas or Non-Gas class in this study [101]. In classification

problems, the probability of a test case belonging to the positive class (e.g., Gas

porosity in this case), is known as the decision threshold value. In most cases, this is

0.5 by default, however in order to produce the new TPR and FPR values, this number

is varied from 0.01 to 0.99 in order to produce a series of TPR and FPR values, which

when plotted consequently produces an ROC curve as can be seen in Figure 41. This

measure shall be used in this study to give an indication of model performance, to

indicate how good the model is at distinguishing between classes. Specifically, how

good the algorithms distinguish between pore types in this study.

6.3.3: RECALL AND PRECISION SCORES

Recall can be defined as how accurately a model predicts a given class [134]. This

given class is also known as the ‘positive class’. In binary classification, it must be

stated which class was selected as the positive class, with the other class then being

referred to as the negative class. Therefore, the results presented for Recall are

presented for the positive class.

Recall is also known as True Positive Rate, is the proportion of actual positive cases

that were correctly identified as positive [134]. This is defined mathematically in

Equation 12 [101]. Recall scores closer to 1 indicate a model which consistently

identifies a selected class correctly. In this study, initially recall is selected for non-Gas

porosity, as these are more damaging to the mechanical performance of LPBF

produced components. In the classification results for Keyhole and Lack of Fusion

pores, Recall is selected for Lack of Fusion porosity, as this form of porosity is more

damaging than Keyhole porosity. Therefore, the Recall results presented in sections

6.4.1 and 6.4.3 are presented for how accurately the models classified Non-Gas

porosity, and the Recall results presented in section 6.4.2 and 6.4.4 are presented for

accurately the models classified Lack of Fusion porosity.

Precision is the ratio of true positives to the total false and true positives, i.e., how

accurate the model can differentiate between incorrect and correct classification of

positives [134]. Precision scores range from 0 to 1, and the closer the value is to 1 the

better, as a high Precision score indicates that the model missed very few positive

cases.

In this study as for the case of Recall, precision is selected for the non-Gas class in

sections 6.4.1 and 6.4.3, and for the Lack of Fusion class in sections 6.4.2 and 6.4.4.

Mathematically precision can be written as [134]:

  

 Equ. 14

6.3.4: F1 SCORES

To improve model performance, either Recall or Precision can be increased, but not

both [134]. Therefore, by increasing recall, precision would be reduced. Therefore, it

is common to use a combination of the two measures. The F1 score is defined as the

harmonic mean between the two measures, mathematically this can be described as

[134]:

 



 



Equ.15

A high F1 score indicates both a high precision, as well as a high recall. A low F1 score

can be due to either a low Precision, or a low Recall. If precision is low, of the cases

predicted as positive, not many of these predictions were correct. If Recall is low, this

indicates many of the actual positives were incorrectly classified as negatives.

F1 scores are a useful metric in order to assess model performance, however a low

F1 score indicates poor performance, and does not say much about whether the

source of the error is low precision or recall, hence when obtaining F1 scores it is

important to keep track of both the individual precision and recall scores also.

6.4: CLASSIFICATION RESULTS

The results section of this chapter is divided into four sections.

• The first section will display the results for the 5-Fold cross validation

examination for Gas/Non-Gas classification on the Gas Flow dataset.

• The second section will display the results for the 5-Fold cross validation

examination for Keyhole/Lack of Fusion classification on the Gas Flow dataset.

• The third section will display the results for Gas/Non-Gas classification on the

Test dataset.

• The fourth section will display the results for Keyhole/Lack of Fusion

classification on the Test dataset.

6.4.1: GAS / NON-GAS 5-FOLD CROSS VALIDATION

This study investigated the performance of the eight classification algorithms applied

to the ‘Gas Flow’ dataset through 5-fold cross validation. This was a binary

classification analysis and investigated the algorithm’s ability to classify Gas type

pores and Non-Gas type pores.

This Gas Flow dataset was obtained from a sectioning study of Ti-6Al-4V cylinders

produced at varying Argon gas flow rates. Recall here is selected for Non-Gas

porosity.

Model:

Accuracy:

AUC:

F1 Score:

Recall:

KNN

0.829±0.006

0.891±0.02

0.859±0.02

0.800±0.03

DTC

0.827±0.007

0.821±0.03

0.860±0.02

0.834±0.03

0.810±0.001

0.879±0.02

0.832±0.02

0.727±0.03

SVM

0.754±0.03

0.886±0.02

0.782±0.05

0.778±0.02

0.823±0.002

0.883±0.02

0.848±0.02

0.759±0.04

MLP

0.820±0.005

0.864±0.02

0.847±0.03

0.759±0.04

XGB

0.839±0.006

0.903±0.02

0.876±0.02

0.850±0.03

0.824±0.007

0.896±0.02

0.860±0.02

0.823±0.04

Average:

0.816±0.008

0.878±0.022

0.846±0.024

0.792±0.052

Table 11: Performance metrics for classifier algorithms applied to Gas Flow Set for

Gas/Non-Gas Classification. Average Score in each metric presented for comparative

purposes. The results are provided for the eight algorithms studied were: K-Nearest

Neighbour (KNN); Decision Tree Classifiers (DTC); Naïve Bayes (NB); Support Vector

Machine (SVM); Logistic Regression (LR); Multi-Layer Perceptron (MLP); Extreme

Gradient Boosted Classification (XGB) and Gradient Boosted Classification (GB)

Table 11 shows the performance of each classifier on the Gas Flow Set using 5-fold

cross validation for Gas/Non-Gas classification. General accuracy refers to the total

number of correct predictions, while AUC refers to the classifiers ability to distinguish

between the two pore types. As detailed in section 6.3.3, Recall measures the

algorithm’s ability to accurately classify Non-Gas porosity, while F1 score measures

the algorithms ability to classify Non-Gas porosity correctly as well as distinguish

between the two classes. Each score contains error bars due to the fivefold cross

validation analysis.

Of the eight classifier algorithms investigated, the two Gradient Boosting algorithms

achieve the highest AUC value, followed by the KNN model. The Extreme Gradient

Boosting Model achieved the highest value in each of the four chosen metrics also,

indicating a high level of accuracy overall, while also demonstrating its ability to

classify non-Gas porosity in the Gas Flow Set, to a high degree of accuracy.

6.4.2: KEYHOLE/LACK OF FUSION 5-FOLD CROSS VALIDATION

This study investigated the performance of the eight classification algorithms applied

to the ‘Gas Flow’ dataset, through 5-fold cross validation. This was a binary

classification analysis and investigated the algorithm’s ability to classify Lack of Fusion

type pores and Keyhole type pores. As detailed earlier the Gas Flow dataset was

obtained from a sectioning study of Ti-6Al-4V cylinders produced at varying Argon gas

flow rates. Recall here is selected for Lack of Fusion porosity.

Model:

Accuracy:

AUC:

F1 Score:

Recall:

KNN

0.632±0.012

0.618±0.037

0.733±0.028

0.767±0.044

DTC

0.698±0.014

0.670±0.039

0.784±0.029

0.788±0.041

0.528±0.002

0.565±0.038

0.532±0.041

0.396±0.042

SVM

0.678±0.000

0.597±0.080

0.807±0.026

1.000±0.000

0.648±0.008

0.702±0.048

0.771±0.032

0.877±0.067

MLP

0.678±0.001

0.503±0.028

0.809±0.024

0.999±0.014

XGB

0.738±0.010

0.790±0.035

0.813±0.024

0.837±0.041

0.759±0.011

0.801±0.031

0.827±0.025

0.864±0.040

Average:

0.670±0.007

0.656±0.042

0.759±0.029

0.816±0.036

Table 12: Performance metrics for classifier algorithms applied to Gas Flow set for

Keyhole/Lack of Fusion Classification. Average Score in each metric presented for

comparative purposes.

Table 12 shows the performance metrics of all eight classifiers on the Gas Flow

dataset 5-fold cross validation experiments. In contrast to table 11, the AUC, F1 Score,

and Recall are all specifically for Lack of Fusion (LOF) Porosity, rather than Keyhole

porosity. This approach was taken, as LOF porosity is the most detrimental form of

porosity, due to its highly irregular geometry promoting crack initiation at these pore

locations.

Similarly, to table 11, Extreme Gradient Boosting Model performed relatively well

across all metrics, with regular Gradient Boosting, in this case outperforming Extreme

Gradient Boosting in each metric. Both the Support Vector Machine and Multi-Layer

Perceptron obtained extremely high Recall values of 1.0 and 0.99 respectively,

however these came at the expense of lower-than-average AUC scores, indicating a

strong bias towards Lack of Fusion porosity in these algorithms. In this cross-validation

experiment, similarly to the Non-Gas/Gas experiment, Extreme Gradient Boosting

performed above average in all measures, however in this case it was outperformed

in each measure by regular Gradient Boosting.

6.4.3: GAS / NON-GAS TEST SET EVALUATION

This study investigated the performance of the eight classification algorithms on the

‘Test Set’ dataset, having been trained upon the ‘Gas Flow’ dataset. This binary

classification analysis investigated the algorithm’s ability to classify ‘Gas’ type pores,

and ‘Non-Gas’ type pores. Recall here is selected for Non-Gas porosity.

As detailed earlier this ‘Test Set’ was obtained from a highly porous sample set of Ti-

6Al-4V cylinders, which were sectioning and examined using the same approach used

to obtain the ‘Gas Flow’ dataset.

Model:

Accuracy:

AUC:

F1 Score:

Recall:

KNN

0.793

0.894

0.838

0.844

DTC

0.793

0.760

0.849

0.986

0.778

0.881

0.884

0.834

SVM

0.778

0.859

0.864

0.771

0.861

0.874

0.861

0.840

MLP

0.861

0.863

0.848

0.844

XGB

0.846

0.898

0.835

0.955

0.846

0.909

0.847

0.934

Average:

0.819

0.867

0.853

0.876

Table 13: Performance metrics for classifier algorithms applied to Test Set for

Gas/Non-Gas Classification. Average Score in each metric presented for

comparative purposes.

The performance of each classifier on the Test Set data for Gas/Non-Gas

classification, is presented in table 12. It can be seen from this table that for each of

the four metric’s evaluated, a different classifier obtained the highest performance,

which contrasts with the Gas Flow Set, where Extreme Gradient Boosted Classifying

scored the highest across all metrics. However, Extreme Gradient Boosting still

records above average scores in Accuracy, AUC and Recall, but not for the F1 score,

indicating that the model tends to produce some false positives which classify gas

porosity, as non-gas porosity.

Figure 42 depicts the Receiver Operator Characteristics (ROC) curve for the test set

performance. The Decision Tree Classifiers (DTC) AUC score is visibly impacted by

its below average Sensitivity (True Positive Rate), in the interval [0.0 to 0.4].

Figure 42: Gas / Non-Gas Pore classification ROC Curve Test set. A higher ROC

curve indicates a larger AUC score and consequently a more accurate classification.

6.4.4: KEYHOLE/LACK OF FUSION TEST SET EVALUATION

This study investigated the performance of the eight classification algorithms on the

‘Test Set’ dataset, having been trained upon the ‘Gas Flow’ dataset. This binary

classification analysis investigated the algorithm’s ability to classify ‘Lack of Fusion’

type pores, and ‘Keyhole’ type pores. Recall here is selected for the Lack of Fusion

porosity.

The Test Set was obtained from a highly porous sample set of Ti-6Al-4V cylinders,

obtained through the same sectioning methodologies as the ‘Gas Flow’ dataset.

Model:

Accuracy:

AUC:

F1 Score:

Recall:

KNN

0.641

0.76

0.713

0.890

DTC

0.641

0.66

0.685

0.773

0.644

0.74

0.701

0.632

SVM

0.644

0.46

0.667

1.000

0.730

0.73

0.651

0.914

MLP

0.730

0.51

0.667

1.000

XGB

0.718

0.78

0.758

0.883

0.702

0.79

0.741

0.853

Average:

0.681

0.72

0.698

0.868

Table 14: Performance metrics for classifier algorithms applied to test set for

Keyhole/Lack of Fusion Classification. Average Score in each metric presented for

comparative purposes.

Due to the smaller size of this dataset the LOF section was up sampled from 125

datapoints to 163. The Test Set dataset contained less pores than the Gas Flow

dataset, due to less samples being available in this sample set, and consequently

fewer cross sections. Up-sampling is a process whereby random samples from a

smaller dataset are duplicated to increase the size of the dataset [135].

Table 14 shows the performance of each classifier on the Test Set for Keyhole/Lack

of Fusion classification, as well as an average score for comparative purposes. In each

metric, a different classifier achieved highest performance. It is interesting to note, that

the two classifiers which achieved perfect Recall scores of 1, both had the two lowest

AUC curve scores, indicating these models had an extreme bias towards classifying

pores as Lack of Fusion pores, while poorly differentiating between the two classes.

For this study, as for the previous data sets investigated, the Extreme Gradient

Boosting classifier was the sole classifier to achieve above average scores for all four

metrics.

Figure 43 depicts the ROC curves for each classifier on the test set for Keyhole/Lack

of Fusion classification. Similar to the ROC curve in the Gas/Non-Gas Test Set

evaluation, the Decision Tree Classifier ROC curve, along with those of the Support

Vector Machine and the Multi-Layer Perceptron also produced poor ROC curves.

Figure 43: Lack of Fusion Pore classification ROC Curve Test set. A higher ROC curve

indicates a larger AUC score and consequently a more accurate classification

6.5: DISCUSSION AND CONCLUSIONS

This study evaluated the use of the supervised machine learning approaches to help

determine the types of porosity present in the Ti-6Al-4V alloy parts, based on cross

sectional analysis of parts using optical microscopy. The performance of the following

eight supervised machine learning algorithms were investigated for the classification

of the porosity: K-Nearest Neighbour (KNN); Decision Tree Classifiers (DTC); Naïve

Bayes (NB); Support Vector Machine (SVM); Logistic Regression (LR); Multi-Layer

Perceptron (MLP); Extreme Gradient Boosted Classification (XGB) and Gradient

Boosted Classification (GB).

In the Gas/Non-Gas cross validation evaluation based on the Gas Flow dataset, it was

found that the Extreme Gradient Boosting model achieved the best performance for

overall accuracy, AUC score, F1 score, and Recall. Recall was defined in this case for

non-Gas porosity. This implies that the Extreme Gradient Boosting model can not only

accurately identify non-Gas pores, but also accurately distinguish them from Gas

pores. The reason for the superior performance of this algorithm on this Gas Flow

dataset, may be due to the large difference in area between the two pore classes. With

Gas pores being far smaller than non-Gas pores, facilitating the distinction between

them.

Upon training the same eight models on the ‘Gas Flow’ dataset, and applying these

algorithms to the Test Set data for Gas/Non-Gas classification, it was found that in

comparison to the above cross validation analysis, that in each metric a different

classifier achieved the highest performance. The Extreme Gradient Boosting classifier

however was found to achieve above average performance for three of the four

metrics, excluding F1 score. This indicating that training upon a separate dataset

reduced the Precision score of this classifier, meaning that it classified some Gas

pores as non-Gas pores. The ROC curves for the classification algorithms in this case

were all similar in behaviour, except for the Decision Tree Classifier, which had a

poorer ROC curve than obtained for the other models.

In the second binary classification for Keyhole / Lack of Fusion pores, F1 scores and

Recall were defined for Lack of Fusion pores. In the cross-validation examination of

the Gas Flow dataset, it was found that the only two algorithms which performed above

average in each metric were the Gradient Boosted and Extreme Gradient Boosted

classifiers. However, in contrast to the initial cross validation examination, the regular

Gradient Boosting outperformed Extreme Gradient boosting. In this comparison it was

interesting to note that some classifiers such as the Support Vector Machine and Multi-

Layer Perceptron, exhibited an extreme bias towards classifying Keyhole pores as

Lack of Fusion, as indicated by their high Recall and low AUC scores.

The final test set involved an evaluation of Keyhole / Lack of Fusion porosity

classification provided some interesting results that mirrored the Gas Flow dataset

cross validation results. Again, the sole classifier to achieve above average results in

all metrics was the Extreme Gradient Boosted classifier, however the regular Gradient

Boosted Classifier did not perform well, in this case. Again, as in the cross-validation

results, the Support Vector Machine and Multi-Layer Perceptron both achieved

extremely high Recall scores, however lower AUC scores, this was also reflected in

their ROC curves. This indicates the same bias towards classifying Keyhole pores as

Lack of Fusion, which was evident in the cross-validation results for these algorithms,

is also found for the ‘Test Set’ evaluation. Through analysis of the eight algorithms

performance in both the cross validation experiments on the Gas Flow dataset, as well

as the ‘Test Set’ evaluations for both binary classification problems, the Extreme

Gradient Boosted classifier exhibited the highest scores of the eight models

investigated. Extreme Gradient Boosted classification achieved above average scores

(except for F1 Scores in the Gas / Non-Gas Test Set evaluation), for all four metric’s

for in both 5-fold cross validation experiments, along with both Test Set evaluation

experiments. As highlighted in the literature review, Extreme Gradient Boosted

classification is widely used for machine learning studies, due to its exceptional

performance in comparison to other classification algorithms. This was also evident in

this analysis of porosity type classification.

It was found that Gas / Non-Gas classification was more accurate, than Keyhole / Lack

of Fusion classification through 5-fold cross validation. This was evident in the

increased average accuracy, AUC, and F1 score, obtained for Gas / Non-Gas

classification. The corresponding average values for each classifier comparing

Keyhole / Lack of Fusion were much smaller as demonstrated in Table 15, except for

recall. Even though recall is larger in the Keyhole / Lack of Fusion classification, this

difference is marginal.

Metric

Gas/Non-Gas

Keyhole/Lack of Fusion

General Accuracy:

0.816

0.670

AUC Score:

0.878

0.656

F1-Score:

0.846

0.759

Recall:

0.792

0.816

Table 15: Average metric scores for all eight classification algorithms in both 5-fold cross

validation experiments obtained using the Gas Flow dataset. The values for the Gas/Non-Gas

classification are noticeably larger

A factor which is likely to help explain this the results in Table 15 is that the area feature

in the Non-Gas class is much larger on average than the Gas class in the initial

classification, due to Keyhole and Lack of Fusion pores being significantly larger than

Gas pores. In the Keyhole / Lack of Fusion classification analysis, the difference in

area between the classes is small.

In summary, the aim of this study was to investigate supervised classification

algorithm’s ability to differentiate between Gas pores and non-gas pores (Keyhole and

Lack of Fusion pores). It is concluded from that the Extreme Gradient Boosted

Classifier performed exceptionally well in differentiating between Gas and Non-Gas

pores. When it was subsequently applied to Keyhole and Lack of Fusion pores, it was

also very successful in distinguishing between these two pore types.

CHAPTER 7: CONCLUSIONS

The aim of this thesis was to assess the impact that Argon gas flow during part printing

using the laser powder bed fusion process (LPBF), has on both the overall level and

type of porosity in Ti-6Al-4V alloy samples. The flow of argon gas was varied at three

levels in a production scale LPBF system (Renishaw RenAM 500M), in order to

evaluate its impact on porosity. Porosity measurement data was obtained based on

the scanning of printed parts using XCT, as well as optical microscopy examination of

sectioned alloy samples. A statistical unsupervised machine learning analysis was

carried out on the resulting datasets. The final section of this thesis involved the

comparison of the performance of eight supervised machine learning classifications

algorithms, to differentiate between the different types of porosity identified, based on

data obtained from optical microscopy (ImageJ) examination of alloy cross sections.

A summary of the main findings and conclusions made within this study are as follows:

• The initial study focused on an investigation of the effect of Argon gas flow rate

during LPBF, on the level of porosity within Ti-6Al-4V samples. It was found

through XCT analysis (verified using Optical Microscopy analysis), that the build

produced at a lower gas flow rate of (26per hour), contained a significantly

increased levels of porosity, relative to that obtained at the medium (31per

hour) and high (36per hour), gas flow rates. It was concluded that the 0.21%

porosity generated at the low gas flow rate, is was most likely due to the lower

gas flow during printing removing fewer process by-products, than the case at

the higher gas flow rates. The deposition of condensate and spatter on the

powder bed prior to laser processing, results in an increased likelihood of

porosity formation. The overall level of porosity generated in the printed alloy

samples obtained at the medium gas flow at 0.03%, was similar to the 0.01%

obtained at the high gas flow rate. This indicated that this medium gas flow rate

is suitable for commercialised manufacturing, while minimising Ar gas usage,

helping to explain as to why it is the Renishaw recommended flow level for use

with the RenAM 500M system.

• XCT analysis was used to provide contour plots, which detailed the average

detected porosity obtained for each cylinder, as plotted at its location on the

build plate. A relatively homogeneous distribution of porosity across the build

plates was demonstrated at the medium and high gas flow rates. At the low

gas flow build however, there were substantial variations in porosity across the

build plate. The contour plots indicating that there was higher porosity for

cylinders printed close to the Ar gas inlet, rather than away from it. This result

is surprising, as it is anticipated that with the deposition of process by-products

such as condensate, that higher levels of deposition would be obtained in the

print bed region away from the Ar gas inlet. There is no clear explanation for

this observation and one possibility would be to use gas flow modelling studies,

to help explain this result.

• A comparison between the level of porosity obtained using the XCT and Optical

Microscopy analysis approaches, was carried out. While a direct comparison

between these two measurement techniques is not possible, due to the

differences in the alloy areas examined (i.e. one cross section versus bulk

sample), as well as the image resolutions of the two methods. Nevertheless,

the optical microscopy images (at a broadly similar magnification), consistently

observed an increased level of porosity, when compared with that obtained

using the XCT data. Using the low gas flow rate as an example, the overall

porosity level in the XCT data was 0.21%, in comparison to the optical

microscopy it was found to be 0.65%. The higher level obtained for the latter,

is most likely due to the lower minimum detectable diameter in the optical

microscopy of approx. 1.2 µm, in comparison to approx. 12.5 µm obtained using

XCT. Thus the ‘smaller’ porosity detected using optical microscopy contributes

to the overall increased level of porosity obtained using this technique.

• While the use of micrograph analysis facilitated the detection of smaller pores

in comparison to XCT, the use of the latter technique for porosity evaluation, is

the strongly preferred approach experimentally. The process of sectioning

materials and polishing them in order to obtain micrograph images is a very

time-consuming process. It also only provides porosity information across

individual cross sections of the total part, in contrast XCT analysis is relatively

rapid, is non-destructive and provides information on porosity within the entire

sample.

• In order to determine the optimal number of clusters present within both the

XCT and Micrograph data, Silhouette score calculations were found to be the

best method for determining the number of natural clusters present within each

dataset. Using this analysis approach, it was found that the optimal number of

clusters present within each of the three porosity datasets, was 2. Although

three classes of microstructural pore (gas, keyhole and lack of fusion) are

normally described for printed alloys in the literature, the optimal value being

determined as 2, may be due to the presence of limited quantities of keyhole

and lack of fusion porosity occurring simultaneously within the Ti-6Al-4V alloy

samples, obtained under the PLBF processing conditions investigated. This

was confirmed based on the microscopy cross sectional examination. The AM

processing conditions required for significant levels of the three types of pore

to form simultaneously in the build, do not appear to have been present under

the LPBF processing conditions investigated.

• In order to understand what forms of porosity were more prevalent at varying

levels of Ar gas flow, GMM clustering was applied to the XCT and microscopy

(ImageJ) porosity data. Following average feature values of both clusters in

each dataset, it was determined that the terms ‘Regular’ and ‘Irregular’ could

be used to refer to the two cluster types. Regular porosity containing majority

gas type porosity, due to its regular shape and smaller geometry, and Irregular

porosity containing majority keyhole and lack of fusion porosity owing to its

irregular geometric features and large average area.

It was shown that Regular pores were the most common type of pore across all

three gas flows. It was also found that builds manufactured at higher gas flow

rates had higher Regular pore proportions than builds constructed at the low

gas flow rates. For example, using the XCT data analysis, it was found that

Regular pores made up 93.4% of the high gas flow build, in comparison to

74.3% in the low gas flow build. It was concluded after visual examination using

optical microscopy that most Irregular pores produced at the high gas flow rate

were keyhole, while most Irregular pores produced at the low gas flow rate were

lack of fusion pores. Table 16 shows the proportion of both clusters at each gas

flow rate, based on the XCT dataset.

Gas Flow Rate:

Regular Pores:

Irregular Pores:

Low (26):

74.3%

25.7%

Medium

(21):

95.4%

4.6%

High (36):

93.4%

6.6%

Table 16: Total proportion of both Regular and Irregular clusters at each gas flow within

the Gas Flow dataset, based on GMM clustering

• Eight supervised classification algorithms were investigated, to compare their

ability to accurately classify the three forms of porosity obtained in Ti-6Al-4V

obtained by additive manufacturing. These were K-Nearest Neighbour;

Decision Tree Classifiers; Naïve Bayes; Support Vector Machine; Logistic

Regression; Multi-Layer Perceptron; Extreme Gradient Boosted Classification

and Gradient Boosted Classification. Each was applied to the optical

microscopy ImageJ Porosity datasets obtained at high and low magnifications

from the Gas Flow test sets, which had been manually labelled. In place of a

multiclass classification two-step binary classification was used. It was found

that Gas/Non-Gas classification was more accurate, than Keyhole/Lack of

Fusion classification through 5-fold cross validation. This was evident in the

increased average accuracy, AUC, and F1 score obtained for Gas / Non-Gas

classification. The corresponding average values for each classifier comparing

Keyhole / Lack of Fusion were much smaller as demonstrated in Table 15,

except for recall. Even though recall is larger in the Keyhole / Lack of Fusion

classification, this difference is marginal.

•

Metric

Gas/Non-Gas

Keyhole/Lack of Fusion

General Accuracy:

0.816

0.670

AUC Score:

0.878

0.656

F1-Score:

0.846

0.759

Recall:

0.792

0.816

Table 17: Average metric scores for all eight classification algorithms in both 5-

fold cross validation experiments upon the Gas Flow dataset. The values for the

Gas/Non-Gas classification are noticeably larger

A factor which is likely to help explain these results is that the area feature in

the Non-Gas class is much larger on average, than obtained for the Gas class

in the initial classification, due to Keyhole and Lack of Fusion pores being

significantly larger than Gas pores. In the Keyhole/Lack of Fusion classification

analysis, the difference in area between the classes is small.

• The eight supervised classification algorithms were compared using their

default parameters. The best performing classifiers based on the examination

of the ‘Test Set’, dataset, were found to be Gradient Boosting, and Extreme

Gradient Boosting, as they each consistently achieving above average scores

in each metric. Extreme Gradient Boosting also performed above average in

each metric for both test set evaluations, except for F1 Score in gas/non-gas

classification, indicating a reduced precision in this instance for non-gas/gas

porosity.

Both the Gradient Boosting model, and the Extreme Gradient Boosting model

achieved the highest AUC scores of all eight models in both Test Set

evaluations, indicating that these models were able to most accurately separate

both pore types in each case. The fact that these models had the best AUC

scores, while also obtaining above average scores in each metric is also

demonstrated. Some models, such as the Multi-Layer Perceptron model and

the Support Vector Machine achieved maximum Recall scores in the

Keyhole/Lack of Fusion Test Set, however the associated AUC scores were

only 0.48 and 0.51 respectively. This indicates that they classed every single

pore in the study as being associated with Lack of Fusion, hence the perfect

recall. This demonstrates an extremely poor analysis performance for both of

these models, despite the maximum Recall values.

In summary therefore the Gradient Boosting, and Extreme Gradient Boosting

were the best performing models in this study, exhibiting above average

behaviour in each of the four metrics: Accuracy; AUC; F1 Score; and Recall.

These two models also performed well in both the Gas Flow dataset, cross

validation experiments.

• Both supervised classification, as well as unsupervised clustering have

difficulties associated with their implementation. Supervised classification

required an initial manual labelling of pores into three independent classes,

which proved to be time consuming. Determining the number of clusters for the

unsupervised clustering proved difficult also, as four separate statistical

techniques had to be implemented. However, the unsupervised clustering

analysis may prove more useful going forward, as it requires no user knowledge

on porosity prior to implementation, in comparison to supervised classification

which requires a large amount of user input.

• In summary, two separate machine learning model approaches were applied to

porosity analysis data, obtained through XCT and micrograph analysis of Ti-

6Al-4V alloy samples. An unsupervised clustering model known as the

Gaussian Mixture Model (GMM), as well as eight supervised classification

models, of which the best performing model was the Extreme Gradient Boosting

Classifier (XGB), were implemented.

Two clusters were identified in each dataset, and GMM clustering was applied.

It was found that the proportion of pores within the ‘Irregular’ cluster in each

dataset increased with decreasing Argon gas flow rate. These Irregular pores

were most likely Lack of Fusion pores, or Keyhole pores.

Extreme Gradient Boosting was identified as the optimal classification algorithm

of the eight implemented on the micrograph porosity dataset. This was due to

its above average result in each of the four classification metrics (general

accuracy, AUC score, F1 score, recall), in both binary classification analyses

on the ‘Test’ dataset. The XGB model also achieved above average results in

each metric in both 5-fold cross validation analyses on the Gas Flow dataset.

7.1 FUTURE WORK

Based on the results from this MSc thesis amongst the potential areas for future

research are:

Process parameters - Within this work, the only additive manufacturing process

parameter varied was that of the Argon gas flow rate. And although the effects of most

process parameters on overall porosity fraction are well studied in the literature, the

effects of process parameters upon the type of porosity, is an area that requires further

study. This could potentially be investigated through a similar method to this thesis, in

XCT scanning components at identical build locations, and sectioning the same

components for ImageJ optical microscopy porosity analysis.

Supervised Approaches - The eight supervised classification algorithms that were

investigated were analysed using their default scikit-learn parameters. In practise, the

performance of a machine learning model can be improved through optimising the

parameters of that model. A more in-depth analysis of their performance could be

obtained through parameter optimisation upon the Gas Flow dataset. This may yield

a more accurate assessment of each models maximum accuracy in the classification

of porosity data obtained from optical microscopy images.

ML model optimisation - As the level of porosity data obtained through optical

microscopy is far larger than that obtained through XCT analysis, the pore class types

across each gas flow could be assessed using the Extreme Gradient Boosting

Classifier. This would be achieved by a labelled subset of the Gas Flow dataset being

used as a training set, and the entire microscopy dataset being used as the test set.

This would be similar to the Regular pore cluster proportion at each gas flow being

analysed through clustering, however this would be a class obtained through

supervised methods. This could yield a more accurate pore type proportion than the

XCT analysis, due to the minimum detectable diameter in optical microscopy being

much less than that obtained using XCT.

APPENDIX A

This appendix provides the BIC scores for each dataset in this study (both

microscopy magnifications and the XCT dataset) at each gas flow rate. This results

in nine graphs in total, with each graph containing the BIC score plotted at cluster

numbers from two to nine. This is plotted for each of the covariance types, as

described in section 5.2.

BIC SCORES

In this three-by-three grid each column represents a gas flow, and each row represents

a data source. Each of the nine graphs, contain four individual line plots for each of

the covariance types. It can be seen from Figure 44 that no clear BIC minimum is

reached in any of the nine graphs, with each containing line plots that appear to

converge to some minimum far beyond the chosen range of clusters. It can also be

seen that in each case, the full covariance GMM produced the minimum BIC line

graph, while spherical covariance produced the largest BIC cluster line graph.

Therefore, as this method does not provide a clear indication of cluster number, a new

method was implemented. However, this result does indicate that full covariance is the

optimal covariance type. Therefore, full covariance shall be implemented in the GMM

implementation section 5.5.

Figure 44: BIC Scores vs Cluster Number for each GMM Covariance matrix. Each

column corresponding to a Gas Flow rate, which each row corresponding to XCT data,

or the two Optical Microscopy data sources

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